John McCutcheon does a Watermelon Song, is that the same as Cooney's? John's starts:
W-A-TER,MELON, What's that spell? (letters are spoken)
Watermelon!!
(spit seeds out here, right into the mic).......

I did a search for Willy the Spider on Google with the phrase children's songs........was sent to a LOT of pages with wonderful songs, and lots of food songs on each page. You might try that. Takes a little effort, but......