Well, here's my 2cents.
I will have to disagree with Mr. Fudd. 270 is most certainly legal in Ontario for small game. Although the projectile diameter is .277, caliber or "bore" is measured off the lands, not the grooves. Therefore .270 is under the .275 restriction.
Like Derk says, .270 good all round rifle. I have taken 2 moose with a .270 with great results.
It's just perhaps a little "big" for 90% of what you want it for...coyotes. The recoil may be an issue as well. The .270 is a necked down 30-06 brass. Sure, dead is dead and it will certainly work for coyote.
The "problem" I see is that .270 you are usually limited in factory ammo to 130 and 150 grain projectiles.
You can read all about the virtues of the .270 by Jack O'Connor in past issues of Outdoor Life. Hey, don't get me wrong, I myself am more "old" and certainly not "fashioned" Heck I regularly shoot .308.
You mentioned the .243 which is an excellent and accurate cartridge for up to medium sized game, including deer and black bear.
Now, here is another suggestion. Have a look at the new kid on the block that's becoming increasing popular and dare I say it...mainstream.
6.5mm Creedmoor. Increasingly more available in a variety of brands of rifles and factory ammo. Excellent results on medium sized game. And, if you want to "punch some paper" out to 1000 yards, it will do that very well.
If you had not mentioned deer/black bear and were looking just at coyotes, I would suggest .223. Ammo, used to be more reasonably priced, but offer many sizes of projectiles, especially if you reload.
Like many things, it's difficult to have "one to do it all"...that's why they make gun safes that will hold 10 or 20+ rifles cause you can never have just one.