Harvard University library has a broadside, not viewable online, but cataloged thus:

BRANNIGAN'S PUP
sung by John O'Neil and John Conroy with great success
no songwriter identified
New York: H.R. Prowell's Book Exhange, 1886.

First line: Now old Mickey Brannigan had a bull pup


I found these lyrics in Irish Song Book, No. 1 (New York: Wehman Bros., 1909), page 116:


BRANNIGAN'S PUP

Now old Mickey Brannigan had a bull-pup.
He was bred of rale elegant stock.
For seventeen hours a battle he fought;
He did, by my soul, by the clock.
His tail was a neat little bit of a stump,
Bow-legged and two crooked eyes.
One look at his ugly-looking mug was enough.
He was the divil himself in disguise.

CHORUS: Bow-ow-ow, what a pup to be sure.
For fighting he'd never give up.
There never was known such a wonderful dog
As Mickey Brannigan's pup.

He tore the tail off Maloney's best coat,
Ate the bustle of Mary Ann Flynn,
And run between young Kitty Mulligan's legs.
Now wasn't that truly a sin?
He caught up the Dutch shoemaker's dog,
And shook him around like a rat.
He murdered Tim Finnegan's beautiful goat,
Ate the tail of McManus' cat.

An Italian came around with an organ one day,
And a monkey tied fast to a string;
And when the pup saw them, he howled with delight,
And made a most wonderful spring.
He upset the monkey, grinder and all,
And bursted the organ inside;
And, be jabers, he tried to swallow the monk,
But he choked on his tail and he died.


There was an album: "Ted Ashlaw—Adirondack Woods Singer," consisting of field recordings, issued by Philo #1022, 1976, which contained a song called MICKEY BRANNIGAN'S PUP.

There was a 78-rpm record, NEVER TAKE THE HORSESHOE FROM THE DOOR b/w BRANNIGAN'S PUP, Decca 25049, made by Pat Harrington with orchestra, which was part of an album called "Irish Come-All-Ye's," 1949.