BY 22 I assume you mean .22 rimfire. Although it is not imposible to take coyote with this cartridge, most coyote hunters use a larger centerfire cartridge similar in caliber. expl 22-250, .223 etc.
Also, coyotes can be difficult to call in close enough for a shot, have a nose second to none and eye site to go with it. add speed and agility and you will have your hands full.
there is a varmint section on this forum that you could probably get a lot more advice and a better idea of what you need to do to prepare yourself for this quarry.
hope this helps a little
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