Songs of Raunch and Ill-Repute page 25 has something similar to the Boogie Woogie / Rockin' Robin:

ALA BOOGY

Mom's in bed, Pop's on top,
Kid's in the cradle yellin', "Shove it to her, Pop."
Ala Boogy -- That's all I crave.

Mom's in bed, Pop's in jail,
Sis's in the corner yellin', "Pussy for sale."
Ala Boogy -- that's all I crave.

Mom's in the kitchen, Pop's locked up,
My hunchback brother has my sister knocked up.
Ala Boogy -- that's all I crave

Got a model T Ford, tank's full of gas,
Mouth's full of titty, and hand's full of ass.
Ala Boogy -- that's all I crave.

Haven't got a nickel, haven't got a dime,
House full of kids, and none of 'em's mine.
Ala Boogy -- that's all I crave.

Way down south in the sycamore timber,
If you can't get it hard, stick it in limber.
Ala Boogy -- that's all I crave.

I've done sung this song till I sweat,
Ain't anybody bought no Ala Boogy yet.
Ala Boogy -- that's all I crave.

Notes: It seems that the commercially successful 1958 "Rockin' Robin" song was a cleaned up version of the bawdy original. The text above is from May 1958.

The "...tank full of gas ... hand full of ass" verse floats independently and has been used as a marching cadence (to the tune of "Sound Off (the Duckworth chant)". The first two verses also appear in other bawdy songs.