The colloquial American-English expression rocking-chair job (also, rarely, rocking-chair work) denotes a sinecure, i.e., an office or position providing an income or other advantage but requiring little or no work.
—Cf. also the expression rocking-chair money.

The earliest occurrences of the expression rocking-chair job, also rocking-chair work, that I have found are as follows, in chronological order:

1-: From the Fall River Daily Herald (Fall River, Massachusetts) of Wednesday 15^th May 1901:

The Consolidated [Railroad Company] is unacquainted with existing conditions. It has been waited upon by no committee of citizens representing various industries; it has heard indirectly, if it has heard at all, that freight rates were regarded as exorbitant, that baggage cars were objectionable as substitutes for so-called “way-trains” and that the postponement of the work on the abolishment of grade crossings was viewed as a joke. Suppose a committee, representing all kinds and all classes were to wait upon the Consolidated and submit grievances? What would come of it? Perhaps nothing would come of it; but perhaps on the other hand such action would amount to as much as sitting still and crossing thumbs and growling. It is true that there are men whose families can prove that they have made fortunes by means of “rocking-chair work,” but rocking-chair work has never changed the face of the map thus far, and it never will.

2-: From a letter to the voters of Latimer County, by D. T. Nowlin, Sr., published in The Wilburton News (Wilburton, Oklahoma) of Friday 29^th March 1907:

I have warned you not to nominate any but good, honest, sober men. Some of my friends asked me to run for Justice of the Peace in Cravens township. I told them I wasn’t qualified to fill the office and I would not have it, if I were, I never did have a rocking chair job; I never had worn out the seat of my pants first. I told them if they could not do any better I would accept the Constable’s office. I believe they are talking of running me for that office; if they give it to me, I will fill it until they can do better.

3-: From Just Yarns, by ‘Doc Bird’, published in The Denver Post (Denver, Colorado) of Monday 24^th February 1908:

A CITY FELLOW WHO WANTED TO BE A RUBE

Once there was a city-broke fellow who had a rocking chair job, but did not know it. He was a regular reader of the farm department of the “Ladies’ Cozy-corner” and soon had it diagnosed that the boys in jeans had the real swansdown snap.

4-: From the following advertisement, published in The Daily Oklahoman (Oklahoma City, Oklahoma) of Wednesday 6^th March 1912:

MALE HELP WANTED.
[…]
We can use some live men at a good advantage; if you are a salary grabber or want a rocking chair job, don’t answer this, but if you can grasp a live one get busy and investigate. Hayers & Green, 310½ North Broadway.

5-: From The Sacramento Star (Sacramento, California) of Thursday 10^th April 1913:

WHAT BUILDING A $24,500,000 AQUEDUCT MEANS
LOOKING AT IT FROM A MENTAL BIRDS-EYE VIEW
[…]
ARTICLE NO. II.
By Harry Ashton.

Los Angeles, April 10.—Having prepared for a campaign of Panama canal caliber, let us see what the 4000 crusaders of pick and shovel encountered in their five years on the Owens river aqueduct.
[…]
The Elizabeth tunnel was the most spectacular job. It took three years, seven months and nine days to crack this hole through the mountain […].
No less strenuous, however, was the work in the blistering desert. Here was where men went mad. Parched under blazing skies in summer, and parched under dry, cold winds in winter, this was no rocking chair job, either.

6-: From The Pacific Commercial Advertiser (Honolulu, Hawaii) of Wednesday 14^th May 1913:

GENERAL FUNSTON HEARS RUMOR OF PROMOTION
Most Active Man in Army Does Not Credit Report That He Will Get Higher Rank.

Brigadier General Funston, U. S. A., commanding the Hawaiian Department, was amused yesterday when a rumor that he was to be made major general and chief of staff of the army, was repeated to him. The general glanced at the single star which adorns each of his shoulders, and then laughed heartily.
“And still they say I don’t like a rocking-chair job,” said the general. “Well, once in a while, a man does like the rocking-chair, just as a change from strenuous hikes, but I don’t think I’m going to be chief of staff for all these alluring rocking-chair prospects.”
Among local army officers the prevailing opinion is that the general still likes the rough-and-ready side of soldiering to which he has been accustomed since 1896, when he went to Cuba with a filibustering expedition and joined the rebels.
“Funston wouldn’t be happy in a rocking chair,” said one of his friends. “He is a born fighting man. The only sit-down assignment he ever had before coming to Honolulu cost him a magnificent gold watch.”

7-: From an article about the newspaper editor and publisher Josephus Daniels (1862-1948), who was appointed as Secretary of the Navy on Wednesday 5^th March 1913, published in The Atchison Daily Globe (Atchison, Kansas) of Tuesday 24^th June 1913:

Mr. Daniels proposes to abolish rocking chair jobs as much as possible, and see that naval officers lead a life intended to keep them fit, and their shooting eye clear.

8-: From Club Notes, published in The San Diego Union (San Diego, California) of Saturday 22^nd November 1913:

Mrs. Helen M. Stoddard, past president of San Diego county Woman’s Christian Temperance Union, and delegate from that body to the “California Dry” convention held in Los Angeles November 19 and 20, returned from the northern city Friday. “I have attended many conventions,” said Mrs. Stoddard, “but never before one so tremendously in earnest. […] A notable feature of the convention was the eagerness of the delegates to do the hard work: they were not seeking rocking-chair jobs.”