I collected a different version when working on a collection of songs of Upstate NY...to the tune of "Irish Washerwoman"

Did you ever go into an Irishman's shanty
Where money was scarce and whisky was plenty
A three legged stool with a table to match
A door in the corner without any latch

You open the door and you will see
Five little cusses a-milkin' a flea
Two at her head and two at her tail
And one little cuss with his head in the pail

Brian O'Lin and his wife and wife's mother
They all went over the bridge together
The bridge fell down and they all tumbled in
We'll find ground at the bottom says Brian O'Lin.

Of course it never goes to the B section of the tune.

Learned from Agnes Warfield, formerly of Cincinnatus, NY
Can be found in "Folk Songs of Upstate New York", KinderFolk Music Publications, 1990
E-mail me if you're interested - lynndeborahk2@aol.com