Below is a close rendition of Andy Stewart's version. I like it a lot better. The rhyming structure is really nice.
There are several words that I'm not certain about:
Avargh and lavic - Andy's recording sounds like this, but ???
humbug - I think is meant to be sort of shooting the bull
jiber - maybe in the same vein as humbug ???
cant - I think means send the cow to be butchered

THE COW THAT ATE THE PIPER

In the year ninety-eight, when our troubles were great,
it was treason to be a Militian.
And the black whiskers said we'll never forget,
and our history shows they were Hessians.
In those troubled times it was a great crime,
and murder it never was riper.
Near the town of Glencree, not an acre from me,
lived one Denny Byrnes, a piper.

Neither wedding nor wake would be worth a shake,
if Denny was first not invited;
for at squeezing the bags or emptying the kegs,
he astonished as well as delighted.
But in these times Denny could not earn a penny,
martial law had him stung like a viper;
and it kept him within till the bones of his skin
grinned through the rags of the piper.

One day it did dawn as Denny crept home
back from a fair at Lethangan;
when what should he see, from the branch of a tree,
but the corpse of a Hessian there hanging.
Says he, "These rogues have good boots, I've no brogues,"
He took hold of the boots with a griper,
and the boots were so tight, and he pulled with such might,
legs and all came away with the piper.

Then Denny did run for fear o' being hung,
til he came to Tim Haley's cabin.
Says Tim from within, "I can't let you in;
you'll be shot if you caught out there rappin'."
So he went to the shed, where the cow was in bed;
he began with a wisp for to wipe her.
They lay down together in seven foot of heather,
and the cow took to hugging the piper.

The day it wore on and Denny did yawn,
then he stripped off the boots from the Hessian;
and the legs, by the law!, he just left in the straw,
then he slipped home with his new possessions.
When breakfast was done Tim sent his young son
to get Denny up like a lamplighter.
When the legs there he saw, he flew up like a jackdaw
and cried, "Daddy, the cow's et the piper."

"Ah, bad luck to the baste, she'd no musical taste
to eat such a jolly auld chanter.
Avargh and lavic, take a lump of a stick,
Drive her off down the road, and we'll cant her."
The neighbors were called, Mrs. Kennedy bawled,
she began for to humbug and jiber.
In sorrow they met and their whistles they wet,
and like divils lamented the piper.

The cow she was drove just a mile or two off,
to a fair at the town of Glenealy.
And there she was sold for four guineas in gold
to the clerk of the parish, Tom Daly.
Then they went to the tent, where the pennies were spent,
Tim being a jolly old swiper;
when who should he see there, playing the Rakes of Kildare,
just your Baltheny Byrnes, the piper.

Then Tim gave a jolt like a half-broken colt,
and he stared at the piper like a gommach.
"I thought by the powers for the last eight hours,
you were playing in the auld cow's stomach."
When Denny observed that the Hessians'd been served,
He began for to humbug and jiber,
and in grandeur they met and their whistles they wet,
and like divils they danced round the piper.