The 1864 manual says a 12 pdr. case round contained 76 musket balls (p. 9). Jack Coggins in his Arms And Equipment Of The Civil War says there were 78 (p. 67). Warren Ripley in his Artillery and Ammunition of the Civil War says there were 78 (p. 379).
I have read that various types of projectiles were used so while the standard seems to have been 78 balls I'd guess that it was sometimes less than that depending on what was available. I know I've seen cross-sections where things like cleaning bullets were used instead of round balls.