There are a bunch of fine CDs containg songs of what dome of my southern friends still rfer to "The Recent Unpleasantness". Bobby Horton, who must be the buffiest Civil War buff in existence has six CDs of "Songs of the CSA" and four pf "Songs of the Union Army/"

David Kincaid's "The Irish Volunteer" is, IMO, superb. He's followed it up with "The Irish-American's Song"--songs of Irish troops on both sides of the conflict.
Folk-Legacy's Barton and Para Civil War CDs are fine stuff, too.