The phrase couldn’t knock the skin off a rice pudding, and variants, are used of a weakling, or of someone or something that is ineffectual. This phrase may have originated in Yorkshire, a county of northern England.
—Synonym: couldn’t punch a hole in a wet Echo.

These are, in chronological order, the earliest occurrences of the phrase couldn’t knock the skin off a rice pudding, and variants, that I have found:

1-: From a letter to the Editor, published in the Yorkshire Telegraph and Star (Sheffield, Yorkshire, England) of Thursday 17^th March 1910:

We certainly do want the law to interfere in the boxing exhibitions—to see that it is a good, honest, square stand up mill, with less feinting and fiddling and exchange of blows that wouldn’t knock the skin off a rice pudding.

2-: From the account of a trial, published in the Yorkshire Telegraph and Star (Sheffield, Yorkshire, England) of Thursday 27^th May 1915:

How a Boy Scout, a member of the Newbold Troop, was, it is alleged, almost strangled by a collier under the influence of drink, during a Whitsuntide encampment at Barlow, was related at Chesterfield County Police Court to-day.
[…]
A number of Boy Scouts were camping in a field at the rear of the Peacock Inn, Barlow, and on Sunday evening, while the lads were in the field, a number of men, including a soldier, went by on the road, kicking a tin can. The soldier was saying something about Kitchener’s Army, and he ran up to three scouts in the field (Tom Slater, Ben Burnett, and George Brunton) and exclaimed, “I can fight you.” The soldier then went into the tent, and, it was alleged, came out with Slater’s food under his arm.
Slater asked for his “snap,” but the soldier denied having taken it, and one of the men—Slater was unable to state which—seized him by the neckerchief, and, lifting him off the ground, swung him round and threw him on his back, leaving him unconscious.
Prisoner alleged that Slater called out that they “could not take the skin off a rice pudding,” but prosecutor denied this.

3-: From the account of a trial, published in The Todmorden & District News (Todmorden, Yorkshire, England) of Friday 8^th July 1921:

Herbert Burley, a neighbour, said that he heard a row while in bed, and he came out and saw that the defendants had Gill on the ground. He took Gill into the house to look at his eye, which was streaming with blood. Then he went out and told the boys they would hear something further about it. John Hutchinson said “Let him come out again and I will have another go at him.” Witness told him to clear off, adding “You couldn’t knock the skin off a rice pudding!” (Laughter.)

4-: From Sports Special (“The Green ’Un”) (Sheffield, Yorkshire, England) of Saturday 25^th March 1922:

AT THE LANE.
Little ’Un who Took a Big Risk.
SOME LIVELY BACK-CHAT.

Scene: Bramall Lane. Occasion: United’s match with the Albion. A big spectator makes noisy remarks and objections.
[…]
Big One (edging the little one again): Gerroff ’oam, an’ get some fertiliser in thi shoes.
Little One (with the light of battle in his eyes): Who’s ta reckon tha’rt trying’ ta shuv abaht, eh?
Big One: Ah don’t know, ticket’s fell off.
Little One: Has it? Well thee push agen an’ it looks like off thee, as big as tha art.
Big One (who accepts the challenge by giving him another push): What, wi’ thee?
Little One: Ah, wi’ me; tha’s many a big tater rotten don’t forget.
Big One (getting annoyed): Go on, get; tha’ can’t knock t’ skin off a rice puddin’.

5-: From The Oxfordshire Weekly News (Chipping Norton, Oxfordshire, England) of Wednesday 17^th January 1923:

MOTOR NOTES.
REPAIR DEPOTS.

Undoubtedly the best way to have one’s car repaired is to do it oneself. This is not always practicable—some owners are too busy; others don’t know how. The large majority don’t know how, or how troublesome the repairing of their old crock can be, and therefore they grumble. They admittedly have a good deal to grumble about—for even the owner of a motor-car, when filling the gear-box and his hands are covered with grease, does not proceed to push the car about by the hood or the best coat of paint without wiping his hands first. The lot of the repair merchant is equally sordid—he can rest assured that even his masterpieces of repair will meet with but grudging praise, a praise tempered by the thought in the repairee’s mind that it cost a lot. A motorist will take his long-suffering motor-car to a repair merchant, and will say unto him, “This rotten machine will not pull the skin off a rice pudding. I’ll want it by two o’clock. Just see if you can put it right.” And he’ll feel really hurt if he is told that his whole method of treatment of the machine is wrong and that it will take some time to put right, and will feel still more aggrieved when he receives a bill “For attention to ill-treated motor-car, etc., £7 18s. 6d.”

6-: From Sweet Nancy, by T. Thompson, published in The Manchester Guardian (Manchester, Lancashire, England) of Wednesday 7^th October 1925—“Mesthur” is the machine-man operating “Sweet Nancy”, a printing machine:

“Mesthur” superintended the dismantling of his pet. It rained “cats and dogs” as they carried her piece by piece and loaded the lorry in the yard. But he shirked nothing. It was nearly dark when “Sweet Nancy” passed out. But “Mesthur” went back to inspect the vacant engine pit. It reminded him of a toothless socket. Then he walked into the boiler-house and sat down to rest. There was a lad outside, he noticed, who was peeping curiously through the ventilator grating. “Mesthur” dosed him generously with the hose-pipe and laughed. His lean sides shook again and again. It was difficult to tell how much was laugh and how much was cough. But in the end the cough overwhelmed the laugh. It was a bad bout. And when he had got through he swore what he would do to that lad if he could lay his hands upon him. But he would in truth have found it hard at that moment to knock the skin off a rice pudding. It was the end of his life of usefulness.

7-: From the account of a trial, published in The Walsall Observer and South Staffordshire Chronicle (Walsall, Staffordshire, England) of Saturday 16^th January 1926:

Jeremiah Wood: If it had been a fight you wouldn’t have lasted two minutes. Why, I could lick three of you before breakfast. You fight, you couldn’t knock the skin off a rice pudding.

8-: From the column From All Quarters, published in the Lancashire Daily Post (Preston, Lancashire, England) of Monday 13^th December 1926:

MAN’S TAUNT.
Man accused at West London Court of striking another man with a plate: He told me that I could not hit the skin off a rice pudding.

9-: From The Kingdom of Golf: Comments on the Game and Local Players, by Austin Savage, published in the Richmond Times-Dispatch (Richmond, Virginia, USA) of Sunday 2^nd January 1927:

The Country Club has plenty of talented golfers who call upon their pro, Ronald Auchterlonie, to “step on the gas” and show them the way over eighteen holes.
Of the numerous foursomes in which Ronald takes part a most interesting one is between Douglas Brashear with Ronald as his partner, against R. B. Augustine, Maurice Langhorne and his dog, a retriever—of sorts.
[…]
Maurice steps up with every intention of slamming a real one off the tee. He hauls the club head back from the ball and bangs into it mercilessly, recoiling backwards from his swing as the ball whizzes off.
His partner, Bob, turns to Ronald and grins. “That’s a nasty one, Ron!” Douglas Brashear retorts that somebody he knows “couldn’t knock the skin off a rice pudding,” and looks at Bob.
“Well, if you folks will turn off that phonograph, I’m ready,” replies Bob, and tees up.