The plural noun Paralympics designates an international athletic competition, modelled on the Olympic Games, for disabled athletes.

Originally for athletes with spinal injury, but later broadened to include other types of disability, the Paralympics take place in the same year as—and now at the same venue as—the Olympics.

The noun Paralympics is composed of:
– the prefix para- in paraplegic (here, this prefix denotes dysfunction—specifically, in paraplegic: dysfunction affecting the lower half of the body)—cf. this prefix in the noun paranoia (i.e., dysfunction of the mind, from ancient Greek νοῦς (= nous), the mind);
– ‑lympics in Olympics.

(In fact, an early synonym of Paralympics was Paraplegic Games—cf., below, the second quotation.)

But, as a result of the broadening of the scope of the games, the noun Paralympics is now frequently apprehended as composed of:
– the prefix para-, used to form terms meaning: analogous or parallel to, but separate from, what is denoted by the root word—cf. this prefix in the adjective parapolitical, meaning: existing parallel to, or outside, the sphere of mainstream politics;
– ‑lympics in Olympics.

The earliest occurrence of the noun Paralympics that I have found is from the following article, published in The Bucks Advertiser and Aylesbury News (Aylesbury, Buckinghamshire, England) of Friday 26^th June 1953 [No. 6,214, page 10, columns 1 to 3]:

“Paralympics” Of 1953—Just What The Doctor Ordered!

In August well over 150 paraplegics will guide their wheelchairs on to the lawns of Stoke Mandeville Hospital 1 and perform feats that ten years ago would have caused most British spinal experts to collapse in amazement on the pavements of Harley-street 2. The 1953 “Paralympics” will justify the claim of a quiet, unassuming doctor, who will be proudly watching, that the days when a wheelchair was virtually a straight-jacket are as dead as Mrs. Squeers’s brimstone spoon 3.
The man whose inspired mission is to prove that, when a man is fated to spend the rest of his life in a wheel-chair, his sporting activities are not finished, is the architect behind these Olympic Games for the disabled—Dr. Ludwig Guttman [sic] 4, O.B.E., Director of Stoke Mandeville’s Spinal Injury Centre.
Dr. Guttman, who cuts through red-tape as enthusiastically as his patients throw the javelin, has torn apart like a whirlwind the old conception of life for the paraplegic.
Minister of Pensions Heathcote Amery [sic] 5 told competitors at the first “Paralympics” last year: “Doctors may prescribe medicine and treatment, but it is the undefeatable spirit of the patients which really helps to produce results.” As a result of Dr. Guttman’s revolutionary “medicine and treatment” his patients have that undefeatable spirit.
It was back in 1944 that the Guttman whirlwind first began to gather impetus. “It became quite certain to me,” he says, “that the methods of physical medicine practised at that time were quite inadequate to restore the physical fitness of paraplegics enough to prepare them for a new life of independence. Radical changes were imperative to remedy what throughout the centuries had been a most unsatisfactory situation.”
As the whirlwind swept on, it cast aside the old methods of recumbency and immobilisation—plaster casts and plaster beds. Says Dr. Guttman: “To-day we may explain this as merely ‘commonsense,’ but then that sense was by no means common.”
The new methods did not pass uncriticised. Some called them harsh. But Dr. Guttman had gathered round him an enthusiastic team of workers, and the new approach began to bring results.
One afternoon late in 1944, Dr. Guttman seated himself in one of his patient’s [sic] wheel-chairs. A spectator may have doubted the doctor’s sanity, for as he propelled the chair with one hand, in the other he waved a walking stick, using the curved end to hit a ball which he chased down the lawn. “Wheel-chair polo” was born. But it was not just a freak sport. As he manœuvred clumsily along the grass Dr. Guttman realised that a sport had been created in which it was the able-bodied person who was the more handicapped, for it is extremely difficult for a non-paraplegic to keep his feet still in the tray of a wheel-chair while taking part in an active sport.
And at the same time it greatly improved the circulation in both the normal and paralysed areas of the patient’s body.
With practice, Dr. Guttman’s wheel-chair polo players gained a competence that amazed all who watched them. The man and his wheel-chair seemed to merge into one. So skilful were they that they invariably beat the teams of able-bodied players they met.
These results were so encouraging that soon other sports were converted by Dr. Guttman and his team. The word wheel-chair prefixed basketball—specially suited to female patients—archery, badminton, javelin-throwing and putting the shot. Organised sport for paraplegics had come to stay.
The same day that the 1948 Olympic Games opened at Wembley the first Inter-Spinal Unit Games took place at Stoke Mandeville. Only two teams competed, but this was enough to cause “The Times” of the following day to register its amazement at the feats of the patients.
In August 1949, for the first time, paralysed sportsmen and women took part in a special section of sports tournament held in Aylesbury. A year later they took part in the Festival of Sport at the Empress Hall, London, where one old lady in the audience, stunned by the demonstration, whispered to her neighbour: “Bless my soul—I thought they were all invalids!”
After the 1951 Inter-Unit games had attracted 126 competitors, Dr. Guttman decided that the time had arrived to make this an international event. “Why not hold Olympics for the disabled?” he asked himself.
As a result a team of Dutch patients took part in last year’s Games, and the number of competitors was up to 150. This year Dr. Guttman has invited teams from eight countries to visit Stoke Mandeville in August—Canada, the U.S.A., France, Belgium, Holland, Finland, Italy and Austria. He has already received the acceptance of the Dutch team.
And this year there is a new item on the programme which shows that the Guttman whirlwind is still roaring through Stoke Mandeville—water polo. A special swimming pool has just been completed and is already being used by fifteen patients. “This has already fully justified my expectations” smiles the man who will stop at nothing to give a new meaning to the lives of his patients.
Anyone who is a bit tired of living should make a point of visiting Stoke Mandeville Hospital. It’s a tonic!—C.A.B.

The second-earliest occurrence of the noun Paralympics—and the earliest occurrence of the noun Paraplegic Games—that I have found are from the following article, published in The Bucks Advertiser and Aylesbury News (Aylesbury, Buckinghamshire, England) of Friday 7^th August 1953 [No. 6,220, page 1, columns 6 & 7]:

All The World There In Wheel-Chairs

All the world will be at Stoke Mandeville to-morrow—in wheelchairs. The flags of five nations will fly alongside the Union Jack at the entrance to Stoke Mandeville Hospital welcoming competitors and visitors to the sixth Stoke Mandeville Paraplegic Games, the wheelchair olympics [sic].
The Paralympics, started at Stoke Mandeville in 1948 with only 26 competitors, have this year become an event attracting worldwide interest.
Teams of wheelchair sportsmen are coming from Finland, Canada, France, Holland, and Israel. Just under 200 will be taking part, including individual competitors from Australia and South Africa.
Great Britain will be represented by teams from Stoke Mandeville, the special spinal settlements and hostels at Watford, Lyme Green Macclesfield, Isleworth and Richmond, and the new spinal unit at Rookwood, Cardiff.
Women’s team from Stoke will compete in archery and swimming on equal terms with men.
Teams of “old boys and girls” of the National Spinal Injuries Centre at Stoke—patients now discharged and living in their own homes—will be coming back to take part in the sporting events.
New swimming pool, built to special design for paraplegic patients, is to be officially opened to-morrow and it is expected that water polo will be played.
In addition there will be wheelchair polo, the pioneer of all paraplegic sport first developed at Stoke, basket ball, which followed soon after, archery, javelin throwing, and putting the shot.
At the start there will a “drive past” of all the competitors who will come on to the field to the sound of the “Stoke Mandeville March” written by Pierre Haas of Boulogne, paraplegic Director of Boulogne Chamber of Commerce. He was one of the leaders of the Resistence [sic] during the war and wrote the March inspired by the unquenchable spirit of the Paralympics.
The “Stoke Mandeville March,” to be heard for the first time to-morrow, will be played by the Central Band of the R.A.F., who are playing throughout the afternoon.
It will also be the first time Stoke Mandeville’s Paralympic Flag will be seen fluttering high over the arena—the letters S.M.G., in white against a green and red ground, surrounded by six gold stars, one for each country taking part in the Games.
On this big day in Stoke Mandeville’s history there will be speeches by the Minister of Pensions, Mr. Heathcote Amery [sic], whose Ministry are handing over the spinal unit to the Oxford Regional Hospital Board at the end of this month, and the Parliamentary Secretary to the Minister of Health, Miss Pat Hornsby-Smith 6, who will present the awards.
The townspeople of Aylesbury whose interest in Stoke Mandeville has always been deeply appreciated by the hospital authorities are invited to come up and watch the Paralympics. No admission fee is being charged but spectators can help the Hospital Sports Fund by buying programmes which will be sold by student nurses.
And you are warned—the organisers are sorry but they have not got sufficient facilities to provide refreshments.
The Canadian team of seven war veterans from Montreal spinal unit arrived last week and have spent part of this week sight-seeing and practising. The Finnish team, accompanied by a doctor arrived on Tuesday. The ten Dutch competitors who are taking part in nearly all the contests arrived front the Dutch Military rehabilitation centre at Aardenburge [sic], Doorn also accompanied by a doctor on Wednesday. They were flown over in a plane of the Dutch Airforce. The French team of two, with two nurses, arrived by air from the Paris Institution Nationale des Invalits [sic], on Wednesday.
The Israel team also flew, arriving yesterday.

Notes:
1 Stoke Mandeville Hospital is located in Aylesbury, Buckinghamshire, England.
2 This refers to the specialists of the medical profession based in and around Harley Street, Marylebone, London.
3 This refers to the compulsory dose of brimstone and treacle administered to the pupils of Dotheboys Hall by Mrs. Squeers, a cruel character in The Life and Adventures of Nicholas Nickleby (1838-39), by the English novelist Charles Dickens (1812-1870).
4 Ludwig Guttmann (1899-1980) was a German-born British neurologist.
5 This refers to the British Conservative politician Derick Heathcoat-Amory (1899-1981), 1^st Viscount Amory, Minister of Pensions from November 1951 to September 1953.
6 This refers to the British Conservative politician Patricia Hornsby-Smith (1914-1985), Baroness Hornsby-Smith, Parliamentary Secretary to the Ministry of Health from November 1951 to January 1957.