My father grew up near, if not in, Appalachia, southern Ohio near the river border with WVA. Here's one he learned as a boy:

While going to St. Ives
I met a man with seven wives
Each wife had seven kids
Each kid had seven cats
Each cat had seven kits
Kits, cats, kids and wives
How many going to St. Ives?

I suspect it has a much earlier source and may have followed the same pathways into the region as the old ballads.