I know I sent you one May song (The Drunken Driver by Ralph Stanley, which I'll let you type up as you wish) but since then I've found two more:

A version of "The Two Sisters" titled "O the Wind and Rain" by Laurie Lewis opens: "Early one morning in the month of May, O the wind and rain." Listen here

The album version of the song "The Federal Soldier" by Gandydancer is not online, but a live recording from 2010 can be heard here. The song opens "One morning, one morning, one morning in May / I heard a young soldier lamenting and say"

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Thanks to cnd for the following pm message
cnd A Song for May 16 Mar 2021 04:10 PM

I know you're not quite to May yet, but I was listening to some music the other day and came across a May song that would be good for your lists once you get there.

THE DRUNKEN DRIVER
by Ralph Stanley
The Drunken Driver by Ralph Stanley ("This awful accident occurred on the twentieth day of May")

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Thank you cnd
The Drunken Driver · Ralph Stanley    https://www.youtube.com/watch?v=bmktp3maRXo