Green’s Dictionary of Slang

Atty Hayes’ goat phr.

In phrases

as old as Atty Hayes’ goat (adj.) [proper name Attiwell Hayes on whose estate this beloved goat lived ‘to be a patriarch’]

(Irish) very old.

[1867		J.E. Carpenter Pop. Readings in Prose & Verse I 160: The Dublin damsel looked as dumbfounded as Atty Hayes’ goat, when it clambered up to the top of Shandon Steeple, and found no grass on the top of it].
1877		N&Q 153: Now most Cork men are familiar with the phrase, ‘As old as Atty Hayes's goat,’ which was commonly applied to one well stricken in years with a hoary head.
1928		Cornhill Mag. 703: The Methuselahs of Southern Ireland were for many a long day described as being ‘as old as Atty Hayes' goat’.
1929		Journal of the Royal Australian Historical Society 15 334: His family had been long settled in Cork, and had given rise to a current phrase, ‘as old as Atty Hayes’ goat,’ which was applied to one well advanced in years.