I remember learning this from a radio programme for schools as Uncle Reuben - it was probably the Singing Together programme, mentioned on other threads. The melody was a hash together of one old-time tune for the verse with the chorus tune being closer to the more familiar Uncle Eph melody.
The song also contained a verse from a completely different song:
Raccoon's got a bushy tail; Possum tail is bare. Rabbit's got no tail at all, But a little bunch of hair.