I think it might help if you gave us the other bits you remember.

Does it happen to have a refrain that goes:

Oh my darling .....
Wait until your mommy comes
Wouldn't you like to suck your thumb
Was ever a man so bored

But the more I cootchy-cootchied so
And walked him up down, to and fro
And I give him everything you know
But the more the darling roared!