There are many songs that can be done that way, but there's a danger of getting very twee about it.

THE WHITE COCKADE should work, as some lines are very clearly from his side (... they advanced me some money ...) and others equally clearly from hers (I'll carve his name ...). But there are also some from a narrator (He pulled out his handkerchief to wipe her flowing eyes). Does that mean that you need three people?

Then there are some songs where it's hard to be sure which party is saying what, e.g. THE VERDANT BRAES OF SKREEN.

Richard