I've used the .12 gauge three inch magnum turkey loads with #4 shot on several coyotes. Out to around 25 yards they killed the coyote but a tracking job was in order to recover the fur.
When using the magnum loads of 4 Buckshot, theres no tracking involved. That stuff will rug a coyote out in a heartbeat, IF you know your gun, choke, and load combinations range limitations. See the Firearms section for the post concerning shotguns and loads.
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