The version I know, circa 1951, is almost identical to the one posted by the person who said "I grew up in the south in the 1930's." I learned it from my father, who grew up in Louisville,KY in the 1920's:

"Once upon a time, the goose drank wine.
A monkey chewed tobacco on a streetcar line.
The streetcar broke. The monkey choked,
And they all went to heaven on a billy goat."

I want to thank the creator and contributors to this thread. It is poignant for me, because it is my only lasting memory of my father. He was estranged from our mother, and I remember him teaching us that poem during one or more visitations. He died, by his own hand, shortly thereafter. Until I recently heard the poem in a TV commercial, I had always assumed it was his own, private creation.

Lastly, I want to thank the creators of mudcat.org for hosting the thread, playgroundsongs.com for citing it, and Google for finding the citation.