Thanks, Jim Dixon.
It is indeed in: Francis & Day's album of famous Irish Songs.
So herewith, the lyrics as they show them. Cheekily copied from Alison's post above, then compared/corrected.


DELANEY'S DONKEY
Words & music by William Hargreaves

Delaney had a donkey ev'ryone admired,
Tempo'rily lazy permanently tired;
A leg at ev'ry corner, balancing its head,
And a tail to let you know which end it wanted to be fed
Riley slyly said "We've underrated it,
Why not train it?" then he took a rag,
Rubbed it, scrubbed it, oiled and embrocated it
Got it to the post and when the starter dropped the flag

There was Riley pushing it, shoving it, and shushing it,
Hogan, Logan ev'ryone in town,
Lined up attacking it, shoving it and smacking it;
They might as well have tried to push the town hall down.
The donkey was eyeing them, openly defying them,
Winking, blinking, twisting out of place,
Riley reversing it, ev'rybody cursing it
The day Delaney's donkey ran the half-mile race .

The muscles of the mighty, never known to flinch,
Didn't move the donkey quarter of an inch
Delaney lay exhausted, hanging round its throat
With a grip just like a Scotchman on a twenty shilling note.
Starter, Carter, lined up all the rest of 'em;
When it saw them, it was willing then.
Raced up, braced up, ready for the best of 'em
They started off to cheer it but it changed its mind again

There was Riley pushing it, shoving it, and shushing it
Hogan Logan, Mary Ann MacGraw,
She started poking it, grabbing it and choking it;
It kicked her in the bustle and it laughed "Hee-Haw!"
The whigs and conservatives, radical superlatives
Lib'rals tories, hurried to the place,
Stood there in unity, helping the community
To push Delaney's donkey in the half-mile race.

The crowd began to cheer it. Rafferty, the judge,
Came up to assist them, still it wouldn't budge.
The jockey who was riding, little John McGee,
Was so thoroughly disgusted he went home to get his tea
Hagan, Fagan, students of psychology,
Swore they'd shift it with some dynamite.
Bought it, brought it, then without apology
The donkey gave a sneeze and blew the darn stuff out of sight

There was Riley pushing it, shoving it, and shushing it,
Hogan Logan all the bally crew,
P'lice and auxil'ary, the Garrison Artillery,
The Second Inniskillings, and the Life Guards, too,
They seized it and harried it, picked it up and carried it,
Cheered it, steered it, to the winning place,
Bookies all drew aside and committed suicide
Because Delaney's donkey won the half-mile race.

X: 1
T: Delaney's Donkey
M: 4/4
L: 1/4
Z: NP 24/09/2017
K: C
G/| C3/4 C/4 C3/4 C/4 cc| A3/4 G// A3/4 B// c z| C3/4 C// C3/4 C// cc| G3/4A//G3/4E//D z/ G/| C3/4 C// C3/4 C// cc| A3/4 G// A3/4 B// c A3/4 B//| c3/4 E// E3/4 E// F3/4 G// A3/4 F//| G3/4 c// c3/4 B// cz| EAcA|^G3/4 A// B3/4 G// A3/4 F// E| EAcA| ^G3/4 A// B3/4 c//Az| cccc| G3/4 A// G3/4 F// E3/4 F// G| A3/4 A// A3/4 A// A3/4 B// c3/4 A//| G3/4 A// G3/4 E// D|| E3/4D//| CCc3/4 B// c| A3/4 G// A3/4 B// c3/4 B// c| CCcc| G3/4 A// G3/4 E// Dz| CC3/4 C// c3/4 B// c| A3/4 G// A3/4 B// c3/4 B// c3/4 A//| B3/4 G// G3/4 G// G3/4 A// B3/4 G//| BAGz/G/| C C3/4 C// c3/4 B// c| A3/4 G// A3/4 B// c3/4 B// c| CCcc| G3/4 A// G3/4 E//Dz| G G3/4 F// E3/4 F//G| A3/4 A// A3/4 G// A3/4 B// c3/4 B//| c3/4 C// C3/4 C// D3/4 E// F3/4 G//| ECCz||
w: De-la-ney had a don-key ev'-ry-one ad-mired, Tem-po'-ri-ly la-zy per-ma-nent-ly tired; A leg at ev-'ry cor-ner, bal-anc-ing its head, And a tail to let you know which end it wan-ted to be fed. Ri-ley sly-ly said "We've un-der-ra-ted it, Why not train it?" then he took a rag, Rubbed it, scrubbed it, oiled and em-bro-ca-ted it Got it to the post and when the star-ter dropped the flag There was Ri-ley push-ing it, shov-ing it, and shush-ing it, Ho-gan, Lo-gan ev'-ry-one in town, Lined up at-tack-ing it, shov-ing it and smack-ing it; They might as well have tried to push the town hall down. The don-key was eye-ing them, op-en-ly def-y-ing them, Wink-ing, blink-ing, twist-ing out of place, Ri-ley re-vers-ing it, ev'-ryb-o-dy curs-ing it The day De-lan-ey's don-key ran the half-mile race .

From Francis & Day's Album of Famous Irish Songs. My copy must be early 1970s as it shows the price as either 6 shillings or 30p. The item number for the book in Francis Day & Hunter's catalogue is "F&D Ltd. 23142" This item is marked "Copyright 1921 by Francis, Day & Hunter Ltd." The tune is not quite as I remember Val Doonican doing it, but for that matter, neither are the words. This is included as it gives an early version from a verifiable source.
NP