This is the way Lisa Null sings it:

I am a man of great influence
And I'm educated to a high degree
I came when small from Donegal
On the Daniel Webster across the sea
In the 14th Ward [(or) Jersey City] I was situated
In a tenement with my brother Dan
By perserverance I elevated
And I rose to the front like a solid man.

CHORUS:
Then come with me and I'll treat you decent
I will get you drunk and I'll fill your can
And on the street every friend I meet
Says there goes Muldoon; he's a solid man.

To every party and every raffle
I always go, an invited guest
As conspicuous as General Grant, me boys
I wear a rosebud all on my breast
I'm called upon to address the meeting
Without regard to clique or clan
I show the constitution with elocution
Because you see, I'm a solid man.

Repeat CHORUS

Lisa Null found it in the singing of a Gaelic singer named Niclos Tobean (Spelling uncertain). This was one of only a couple of English songs in his repertoire. It can also be found in Philip Foner, Labor Songs of the Nineteeth Century. And Mick Maloney sings it and has an extra verse.