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The answer to the question depends on a few factors, but as a general rule you should be ok to about 40-45 yards with a good choke/load combination. Through experimenting with different loads you may even find a load that will deliver the goods out past 50 or even 60 yards or so. Keep in mind though that a shotgun shoots small round pellets at a relatively low velocity (1250- 1350 fps). Small round pellets don't retain speed/energy very well so they run out of steam pretty fast. Just hitting him doesn't ensure you have enough energy to kill him. Most people have found that copper plated lead BB's do quiet well and others like #4 buck. I have used both loads and they work fine. Hevi-Shot has also developed a load specifically for coyotes called "Dead Coyote!" This load in 3" contains 52, T sized pellets and shoots at about 1350 fps. The pellets are made of a Tungsten and Nickle and is denser/heavier than lead. Being denser helps it retain it's velocity/energy better than lead. It's expensive but very effective. As you mentioned, you are familiar with patterning your shotgun. I would get some of these loads and pattern them with different chokes and just decide from there what is a reasonable limit for your best choke/load combination. Keepin mind the vitals on a coyote are pretty small and a fox is considerably smaller.
You can also use the search funtion here on PM for more good stuff on shotguns and loads. Plenty of very knowledgable folks around here for sure. Glad to have you join up and hope you have a great season /ubbthreads/images/graemlins/grinning-smiley-003.gif. We like pictures.
Welcome
Byron /ubbthreads/images/graemlins/grin.gif