You will eventually obtain the Six Shooter revolver by defeating the Cowboy Security Guard Psychopath in the South Plaza. Be sure to hold on to this weapon, which can be found on the sawing board he dies on. You can only have one at any time like all Psychopath weapons, so if you try to exit and re-enter the area to get an extra Six Shooter, you won't find anything on there until you lose the one you're carrying (or that your Co-Op partner is carrying). This weapon is extremely powerful, more so than any rifle other than the Sniper Rifle, and also boasts a great rate of fire. With this weapon, you can easily take out most Psychopaths by simply corner shooting, or in some cases just repeatedly shooting them as most Psychos will be stunned for a brief moment by each shot.