Used to sing these songs to my kids when they were little... and that was a long time ago! I've several versions of "Cotton-eye Joe" a lullaby from the mountains of Tennessee accordng to MORE BURL IVES SONGS, Ballantine Books, 1966, and A TREASURY OF FOLK SONGS, Bantam Books,1948. The verse about a jaybird dying from the whooping cough does not appear in either version, and the meter is such that it would be very difficult to make the line fit into this tune.

In my version of "Buckeye Jim", also a lullaby from the southern Appalachians, which I got from FOLK SONG: USA, by John and Alan Lomax, the 3rd verse is: "Way down yonder in a wooden trough, An old woman died of the whooping cough." The other verses (this version has 4 in all) have references to jay birds, bluebirds, blue jays, and red birds (along with a green bullfrog!) It's quite possible that some singers substituted "jaybird" for "old woman" (it actually scans better that way.)

Another one I used to sing to the kids was "Bile Them Cabbage Down" (found in FOLK SONGS OF NORTH AMERICA, by Alan Lomax) which has this verse: "Jaybird died with the whoopin' cough, Sparrow died with the colic. 'Long come a frog with a fiddle on his back, Inquirin' his way to the frolic."

I'll be happy to post words and chords to any or all of these songs if anyone wants them, but I'd guess they're in the DigiTrad data base (I didn't take time to look for them there.)