My grandmother, who was from Tenneseee (but moved to Idaho at a young age) used to sing a song she said her mother used to sing to her. I've been curious about it for many years. It went something like this:

Little black bug came hopping home rigdom bob a little kayro fell in the well and broke his back bone rigdom bob a little kayro

I'm in the nayro captain kayro I'm in the nayro cairo rigdom rigdom bob a lotta rigdom rigdom bob a little kayro

There may have been more verses, I don't remember. The meter seems to match that of what is described in this thread. I had no idea it was derived from Froggy Went a-Courting, but it makes sense. Thanks to all of you who have shared.