RE: dead coyote loads?
You don't NEED a specific choke for dead coyote loads, BUT you WILL need to pattern your gun with the different choke tubes that you do have. You can use your regular 'ol smooth bore shotgun with dead coyote loads.
IMO, good 'ol 3" #4 buckshot is almost as good and one heck of a lot cheaper than the dead coyote loads. You still need to pattern your gun with it as well, to find your best pattern. With the #4 buck, and a good pattern, 50 yards on a broadside shot will do the trick. Dead coyote loadswill stretch that out a few more yards.
If you're wanting to buy a new .22 mag., go for it. It wouldn't be my first choice for squirrels or coyotes, BUT it will work for both.