"The Civil War Music Collectors Edition" (Time-Life 1991) is an excellent CD set containing all forms of music vocal and instrumental from the period.
Another CD that is reasonably available is Songs of the Civil War" by The Cumberland Three (This was John Stewart's group before he joined the Kingston Trio).
Keith & Rusty McNeil have a collection of about 60 Civil War songs (check out their web site, they also have collections of songs from other periods in US history)
2 Cds by Dave Para & Cathy Barton described in a thread last summer or fall.
Also if you are in a library You can look for:
Singing Soldiers: A History of the Civil War in Song by Paul Glass, 1964, republished by DaCapo Press in 1975 (isbn 0-306-80021-7. This has over 100 songs
Sound Off : Soldier Songs from the Revolution to World War II by E. A Dolph, 1942 Farrar & Rinehart (originally published in 1929 & updated in 1942 to include WWII material)
Don't forget Irwin Silber's collection mentioned near the top of the thread.