I think this was from Chicago (late 50's) where my sisters were little but it might be from Saint Louis (early 60's) where I was little, but I don't think so. I don't remember jumping rope to it, I remember hearing my sisters singing it to me and saying it was a jumprope song. It is almost identical to Guest, Mary's, above, late 50's Michigan. We sang it Hudge, Fudge, which might be the way it was sung and might be us from being half Hungarian, Hogy vagy (pronounced roughly hodge fudge if you kind of "y" instead of "g" the end of each word.

Hudge, Fudge, Call the Judge
Mama got a newborn baby
Not a boy, not a girl,
Just an ordinary baby

Wrap it up in tissue paper
Send it down the elevator
First floor-stop
Second floor-stop
Third floor- shut the door
Momma don't want the baby no more