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:
Every pair of sandalwood-handled six-shooters strapped to the hips of an experienced gunslinger is an heirloom that has been passed from father to son for almost thirty generations. These single-action pistols are cast from burnished steel and fit into lined holsters of hand-stitched, tooled leather. The throat of each holster is carefully shaped and rolled to allow for easy holstering and a fast draw. The two gunbelts to which a gunslinger's holsters are attached are worn crisscrossed over the hips so that the holsters sit low, at the perfect angle for drawing.
True to their names, each gun's cylinder contains six chambers and fires a hand-thrown shell similar in size and weight to that shot by a Winchester .452. Once the gun has been fired, the hammer must be cocked to make the cylinder revolve. Although they are extremely powerful, these guns are perfectly balanced. They sit easily in the hand and their action is smooth and reliable. But although every one of these sandalwood-handled pistols is invaluable, there is one pair that is legendary. Passed down through the line of Eld for almost 700 years, they are known as the guns of Deschain.
- The Dark Tower: The Gunslinger Born, Robin Furth
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.
1Ancient Sword Rage's answer was posted before this one, and it is correct, so I accepted his, but posted mine so that all the information is available. I offered him this picture, but he thought it would be improper to use information I provided, and told me to post it as a self-answer. Please consider upvoting his answer.
2I think this shows us another example of King's lack of knowledge of guns. The assertion that gunslingers use Winchester .45 ammo ignores the facts (as I understand them) that in the 19th century, when guns like this were made, Winchester .45 cartridges were ammo for rifles, not pistols, and although Winchester now makes .45 ammo for handguns, it is designed for semi automatic handguns, and can't be used in revolvers without special adapters called "half-moon clips". The descriptions in the books make it clear that Roland isn't using these clips.