My granny used to sing this song to us while we sat on the porch of our beach house in Garden City beach S.C. She'd play her ukulele and sing.

"My man's a garbage man
he cleans the garbage cans
He smell like garbage too
Mmmmmm, I say he do
And in our future life
We gonna he man and wife........"

That's all I can remember, hence my search that led me to this sight. Her brother was a piano player for Tommy Dorsey's orchestra back in the 40's.

Another one I can remember is:

"Rosie had a body like a toothpick
And a neck like a giraffe
Rosie, where art thou going?
Upstairs to take a bath.
Lord have mercy! Oh, my soul!
There goes Rosie right down the hole!"