In my experience:
Anytime you hunt in brushy areas or will have running shots, you want a 3-9 or less for the field of view. (35+ ft field of view at 100 yards). I put a 2-7 on my deer rifle after having trouble finding a moving deer in the brush with a 4.5-14. I got the deer, but realized my scope was a handicap.
If you expect standing shots or longer distances, magnification is nice, but I wouldn't go higher than 4-16, unless it is a dedicated long range gun.
I think the ultimate deer hunting scope would be a 2.5-10 Nikon monarch with the BDC reticle. Wider field of view than a 3-9 with more top end, and the optics are awesome. I don't see any reason why this wouldn't make a good coyote hunting scope.
They make a 3-12 also, this may even be better on a .22-250. As a bonus this one has side focus.
I have a 4-16 on my .223. It isn't a bad scope for me, I hunt coyotes in some pretty wide open areas. Unfortunatley, it is a cheap BSA. Pretty good for the money, but I'd like to upgrade.
Bottom line, I think field of view is important wihen stuff gets clot.
2-7, 2.5-10, 3-9 for close in shots
3-12 up to 4-16 good all around
6-18 or 6-24 for long range. (will be a handicap on close in or moving stuff)
This is why you need two guns, one setup for the more intimate surroundings, and one to deliver mail to the next zipcode.