Number 1368 in the Roud Folk Song Index, and found, it appears, pretty much wherever English is spoken.

Short text with music and description of game:

Bittersweet Volume VI, No. 1, Fall 1978: We've got a Pig in the Parlor: Ozark Play Party Games

Set from Almeda Riddle at the John Quincy Wolf Folklore Collection:

Green Gravel