'Down By The Riverside'.

I doubt he'd have been bothered with Appalacian stuff - there's a sub-plot in an early movie, where 'hillbilly music', ie Appalacian/Celtic gets a lot of shade - 'One More Day' is the song he doesn't sing. Sounds like one from Elvis' slush pile

https://youtu.be/oB9YAVEqWrY