There are several different rifles that make good coyote hunting rifles. Everyone has their preference as to what kind they use. It doesn't take a lot of power to knock down a coyote, therefore there are a lot of guns we can choose from to hunt with. Rimfire and centerfire both are capable of killing a coyote.
Rimfire rifles are named for the way the firing pin strikes the edge of the rim when it is fired. These rifles are smaller and don't produce the knockdown like the more modern centerfire. The most popular rimfire rifle is the .22LR. Most of you have probably heard of this and might even have one. They are good for killing small game like rabbits and squirrels, but are capable of killing a coyote. Larger rimfire rifles were made, but have mostly been replaced by centerfire rifles. A rimfire would be great for a youngster who is new to guns and hunting.
Centerfire rifles are much more popular for hunting than rimfire, because of their accuracy, bullet size, and becauase they make great long range rifles. The best deer rifle is usually a centerfire. These guns come in a wide range of caliber sizes, so you can find one to kill just about anything. I use a .243 win with a 55 grain ballistic tip bullet to do my predator hunting, because of their accuracy and smaller size. However, don't underestimate these rifles, I use this same gun for deer hunting, just a different grain size. Anything bigger than this is probably going to be overkill for any kind of predator hunting. Another similar size is a 22-250, which is another accurate, flat shooting gun that is great for small game.
There are plenty of coyote hunting rifles to choose from, this is completely up to you. If you have a bigger budget, you might even consider semi-auto mp or SKS. Many people enjoy these because they add a little fun to coyote hunting. Just be aware of the laws in your area and know what is allowed.