I'm reading Marvel's The Dark Tower comics for the first time, and in the miniseries The Gunslinger Born, I found this tidbit, which clearly states that gunslingers carry single action revolvers:
Although this image comes from a section describing the different guns of gunslingers (practice guns, apprentice guns, gunslingers' guns, and the guns of Deschain - aka Roland's guns), and Roland's guns are listed separately, it is made clear that all gunslinger guns work the same way and have the same mechanical design. Roland's guns are simply more ornate and made from higher quality metal.
Note: Because I don't like answering my own questions (it makes me feel dirty), I made this answer Community Wiki, so I won't get rep from it.