Here's the oldest version of the song I can find.

From Songs of Ireland and Other Lands (New York: D. & J. Sadlier & Co., 1847), page 103:

THE COW THAT ATE THE PIPER.

In the year '98, when our troubles were great,
And it was treason to be a Milesian,
That black-whisker'd set we will never forget,
Though history tells us they were Hessian.
In this troublesome time, oh! 'twas a great crime,
And murder never was riper,
At the side of Glenshee, not an acre from me,
There lived one Denny Byrne, a piper.

Neither wedding nor wake would be worth a shake,
Where Denny was not first invited.
At squeezing the bags and emptying the kegs,
He astonished as well as delighted.
In these times poor Denny could not earn one penny.
Martial law had him stung like a viper.
They kept him within till the bones and the skin
Were grinning thro' the rags of the piper.

One evening in June, as he was going home,
After the fair of Rathnagan,
What should he see from the branch of a tree,
But the corpse of a Hessian there hanging.
Says Denny, "Those rogues have boots, I've brogues."
On the boots then he laid such a griper.
He pulled with such might, and the boots were so tight,
That legs and boots came away with the piper.

Then Denny did run, for fear of being hung,
Till he came to Tim Kennedy's cabin.
Says Tim from within, "I can't let you in.
You'll be shot if you're caught there a rapping."
He went to the shed, where the cow was in bed.
With a wisp he began for to wipe her.
They lay down together on a seven-foot feather,
And the cow fell a hugging the piper.

Then Denny did yawn, as the day it did dawn,
And he streel'd off the boots of the Hessian.
The legs, by the law, he left on the straw
And he gave them leg-bail for his mission.
When the breakfast was done, Tim sent out his son,
To make Denny jump up like a lamplighter.
When the legs there he saw, he roar'd like a jackdaw,
"Oh, daddy! the cow's ate the piper!"

"Musha bad luck on the beast! She'd a musical taste,
For to eat such a beautiful chanter.
Arrah! Patrick avic, take a lump of a stick,
Drive her off to Glenhealy. We'll cant her."
Mrs. Kennedy bawl'd, and the neighbors were call'd.
They began for to humbug and gibe her.
To the churchyard Tim walked, with the legs in a box,
And the cow will be hung for the piper.

The cow she was drove a mile or two off,
To the fair at the side of Glenhealy,
And there she was sold for four guineas in gold,
To the clerk of the parish, Tim Daly.
They went to a tent. The luck-penny was spent,
The clerk being a jolly old swiper.
Who d'ye think was there, playing the "Rakes of Kildare,"
But poor Denny Byrne, the piper!

Then Tim gave a bolt, like a half-drunken colt.
At the piper he gazed like a gommack,.
He said, "By the powers! I thought these eight hours
You were playing in driman dhu's stomach!"
Then Denny observed how the Hessian was served,
And they all wish'd Nick's cure to the griper.
For grandeur they met, their whistles they wet,
And like devils they danced round the piper.


[The above text is very close to that found in the Bodleian collection, Harding B 11(2916), where it is called THE COW EAT THE PIPER.]