Here in this part of the East, in NY we can use any rifle in centerfire (as long as you are not in a shotgun only area for deer hunting and a deer season is open) or rimfire at night for Predators. We can also use a shotgun with any shot size.
A .22 rimfire will kill a Coyote. It will even kill a deer and it will even kill a large cow! Think about this though: You know about a 32 point buck that is coming out in an apple orchard every night at the same time. If a .22 rimfire is legal to shoot deer with would you take your's out to shoot this buck? Remember that it will drop him in his tracks if you hit him right. Remember also that it will, and even more often wack him and he will run off never to be seen again. Its not a matter if they will kill a Coyote, its a matter of how many do you want to lose? If you are limited, pick the shotgun. You will collect many more Coyotes!
Tim