"The Watermelon Smiling On The Vine," Thomas P. Westendorf, ©1882.

Here is a page where you can hear a recording made by Sam Bell in 1939: Click here.

It's part of American Memory from the Library of Congress, which looks like a very useful website. I plan to bookmark it.

This seems to be a field recording which would be very hard to transcribe, but if you end up learning any more lyrics from it, please post them here.