Wayne Erbsen has a whole series of tapes of 19th-century music--I know you can get them at a lot of battlefields and souvenir shops but I'm sure he's got a website. If you want to learn tunes & lyrics, they're great.

Cathy Barton and Dave Para from Missouri also recorded a lot of Civil War (and pre-Civil War) music from both sides of the issue.

My personal favorite Civil War songs (which aren't ballads, but oh, well) are "Vacant Chair", "Just Before the Battle, Mother", "Prairie Grove", and, although it's a bit later, "Faded Coat of Blue".