in our area of south western Ontario coyotes are run with dogs and a mix of mostly rifles and a few shotguns . they are used on the close shots or in brush. as for shot sizes every shotgun has its own preference for a given choke and it is up to you to find the diet it likes . i would use the chokes that you have for the gun and try various buckshot loads till you come up with one that throws a decent pattern . if that does not work buy the dead coyote choke but i would not count on it being a magic wand .slugs are another option doubling or tripling the distance you can take them down .