Here are three more ideas:

1. "The Cherry Tree Carol", Child #54

2. A vaguely remembered parody of Woodie Guthrie's "Union Maid", with the only fragments I remember being these:
   There once was an apple maid
   ...
   The apple maid was wise
   To the ways of Northern Spys
I thought I had seen it in Rise Up Singing, but it's not there.

3. The Bulgarian song "Dilmano Dilbero", about the production of red peppers (botanically a fruit though treated as a vegetable). I was surprised how many versions of this that I don't like are on You Tube. After sampling over a dozen, I decided that this one from the Yale University Slavic Chorus obligatory blue clicky is, to my taste, fairly good and is also decently recorded. My taste, however, was formed listening to the Pennywhistlers do this, and I haven't found their version on-line. The page at another blue clicky gives the following transliteration and translation:
Dilmano dilbero - this is a girl's name and/or a play with the name
kazhi mi kak se sadi pipero. - tell me how the peppers are planted
Da tsafti da varzhe da beresh ka sakash - so that they blossom and give fruit, fruit that you can pick whenever you want
Pomuni go, pobutsni go, pomuni go, pobutsni go - put it in the soil and push a little, put it in the soil and push a little (this is a bit rough translation)
Teta kak se sadi pipero - that is how the pepper is planted