To answer the question, you bet, sure it would, but there are many other alternatives and there are many pros and cons to your choice, if i may suggest a few pros
1. You will be able to own one rifle to do nearly all of your North American Big game hunting
2. You shouldnt have to track your coyotes very far.
3. This caliber would come in very handy if you have very long shots.
a few of the cons
1. ammo would be a bit pricey
2. large holes if your hunting them for the fur
3. people always telling you its more "gun than you need"
I actually prefer my .300 win mag, it has a very wide range of bullet weights and styles with which i can reload it with, any where from 110 to 220 grain. I have used my .300 for everything from prairie dogs to Whitetails, and hope to one day take an Elk with it.
It is very flat shooting with the 110 grain bullets, has decent ballistic coefficents, will also takeall North American Big game except maybe the dangerous kind, I would want a .338 for those.
If you are new to this, I would actually recommend a 30-06, it will kill anything with antlers and the ammo is considerable cheaper.
another great alternative today is to purchase a Thompson Contender, they are a beautiful piece of craftsmanship, extremely accurate and you can purchase different barrels, ie....nearly all rifle calibers,shotgun,and muzzleloader. I am actually thinking of selling all of my guns and buying one Contender to handle the bulk of my hunting, I would have to keep the Benelli.
I shot these coyotes with my .300 this winter.