Muskets were still used in the American Civil war, but most had moved on to Rifles, though many were single shot long rifles.

http://en.wikipedia.org/wiki/List_of_weapons_in_the_American_Civil_War

Repeater Rifles were still fairly new most only having been invented shortly before the war, and some being invented during the war. And they were for the most part limited to the arsenal of the Union Army as that was where the factories were. The South had to buy cheaper/older weapons or make/modify simpler ones not having the industrial infrastructure to make many of the more complicated weapons.