Coyote hunting in thick cover has a lot more in common with waterfowl hunting than it does with hunting for turkeys. Coyotes present a variety of fast-moving, coming, going, and crossing shots. Moderately tight patterns are preferred over super tight turkey chokes. Both modern 3.5" autoloading and double-barreled shotguns are particularly well suited for hunting coyotes.
The ability to hold 5 rounds in the gun's magazine is over-rated. From experience, reloading an O/U or a 3-shot auto in the thick of a good stand and killing multiples is not an issue if you're prepared. The shotguns shown here are the Browning Cynergy 3.5 and Beretta Onyx 3.5.