MEANING

The phrase donkey’s years means a very long time.

ORIGIN

This expression is inseparable from donkey’s ears. In fact, these two expressions were originally a single one, donkey’s years being simply a dialectal pronunciation of donkey’s ears—or the other way around.

And donkey’s ears/years (also donkeys’ ears/years) was part of a proverbial rural phrase which ran years and years, and donkey’s ears/years (ago).

The earliest occurrence of donkey’s years that I have found is from the account of the trial of William Dear and George Sheppard, charged with stealing horsehair from Salisbury Infirmary, published in The Salisbury Times, and South Wilts Gazette (Salisbury, Wiltshire, England) of Saturday 1^st July 1876—the following is from an exchange between George Sheppard and a policeman:

Sheppard (to witness): Didn’t Dear make a statement before that?—I asked Dear when he arrived at the Station to account for the possession of the hair, and he said “it was an old mattrass [sic] that belonged to my brother who died in the West Indies.”
Didn’t you ask him how long he had in his possession?
I can’t recollect that. I might have done so.
Didn’t he say for years and years and donkeys years?
I can’t tell. He said he had it a long time.

The earliest occurrence of donkey’s ears that I have found is from In Gipsy Tents (Edinburgh: William P. Nimmo & Co., 1880), an account by Francis Hindes Groome (1851-1902) of his travels with the Gipsies—the author felt the need to explain to the reader the expression that a certain Silvanus was using:

“I have not set eyes on him for donkey’s ears.” [i.e. long years].

The following comments are from the Appendix to A Warwickshire word-book comprising obsolescent and dialect words, colloquialisms, etc. gathered from oral relation, and collated with accordant works (London: Published for the English Dialect Society by Henry Frowde, 1896), by G. F. Northall:

Years and years, and donkeys’ years (? ears). This is a figurative expression for ‘a very long time.’ As the death of a donkey is supposed to be a most rare event, its ‘years’ may serve as an illustration of duration. But ‘ears’ (and the ears of a donkey are long) is often pronounced years, whilst ‘years’ is as often pronounced ears.

And, in 1914, a contributor to Report and Transactions of the Devonshire Association for the Advancement of Science, Literature and Art wrote the following:

The well-known expression, “Us an’t zeed ’e vor years an’ donkeys’-years,” is a play upon the words “year” and “ear,” which are both pronounced alike, yurr, in the dialect.

The same association had already discussed the origin of the expression; a contributor had written the following in 1910:

Donkeys’-years. I should like to protest against the explanation of this expression given in last year’s Report […]. In my opinion it does refer to the donkey’s ears, ‘because they’m long’; and it is a play on the words ear and year. It is just the sort of West-country joke that is made and loved, and handed on from generation to generation. If it had meant anything so dull as the long life of a donkey, it would have deservedly been forgotten as soon as possible after its invention. Its humour kept it alive.

In Notes and Queries: A Medium of Intercommunication for Literary Men, General Readers, etc. (London: Published by The Times Publishing Company) of March 1920, a certain William Self-Weeks also wrote that the expression originally referred to the donkey’s ears:

Donkeys’ Years: a very long time.
[Self-Weeks first refers to a previous contribution.] At the second reference, B. B. states that he has heard this expression for at least forty years in Wiltshire but never in London. I have a cutting from The Standard newspaper of Jan. 21, 1896, which contains the report of a case at the Bow Street Police Court. In the course of the examination of a witness the following occurs:—
“Mr Bodkin: How long ago is it since you first borrowed money from Prisoner?
“Witness: Years and years: donkeys’ ears ago (laughter). It was long before I came of age.”
The expression is noted in Prof. Wright’s ‘Dialect Dictionary,’ as in use in Oxfordshire, and the following quotation given from the Dorchester Parish Magazine (presumably Dorchester in Oxfordshire) for April, 1896: “For years, long years, and to use a well-known local expression, donkeys’ ears”.
The expression is also current in the Isle of Wight. I am over 60, and the expression is familiar to me as in use there as long as I can recollect anything. I am quite satisfied that it is not a piece of modern slang, but a proverbial expression of long standing. It invariably ran “Years and years, and donkeys’ years ago.” There is a tendency in the Isle of Wight dialect to prefix a y to words beginning with a vowel, e.g. “yarm,” the arm; “yeal,” ale; “yeaprun,” an apron; “yet,” to eat. This tendency in the case of “ears” has existed as far back as 1566 as evidenced by the following entry in the inventory taken in that year of the goods and chattels of Sir Richard Worsley of Appuldurcombe (Appendix B. to ‘The Undercliff of the Isle of Wight,’ by J. L. Whitehead, M. D. London, Simpkin, 1911): “2 basons wᵗʰ yeares to them”.

But, as G. F. Northall concluded in the above-mentioned wordbook after writing “‘ears’ […] is often pronounced years, whilst ‘years’ is as often pronounced ears”:

Such is human perversity. The reader must kindly take his own view of the equivoque.