I've found a few more titles in my notes. All of these were mentioned in print before 1900:

The Dying Californian
Comin' Through the Rye
Turkey in the Straw
Gal on a Log
The Old Fat Gal
Snowbird on the Ash Bank
Old Dan Tucker
Clack Satin [sic]

"Comin' through the Rye" is Scottish. Most or all the rest appear to be American-made.