We've got tons of cats here. We've got a huge cougar population since the libs voted out hound hunting. This cat was taken about 10 miles from my house. The guy on the right got a special hound permit to kill one. I know both of these guys.
We kill a lot of yotes with whatever we have. The biggest problem is finding a bullet that works without blowing them up. Will you be hunting where you have to worry about bullet travel after you hit, or miss the coyote. If you are alone in the wide open spaces I would consider a FMJ bullet. With a 308 a FMJ will surly kill them, if you stay out of the guts, without making a huge exit hole.
I use a 243 with 75 gr. ballistic tips and often blow them up if I don't hit bone, but I like that the bullet stops after I hit something.
A friend uses a 6mm with soft points and usually does qwite well.
As I sit and glass, which is common for hunters out west, I have sort of quickly discovered something I never learned when I was younger.
In my youth I had enthusiasm and spirit. In my middle to advancing years I have creaky knees, arthritis, and I tire more easily than I used to. Where I used to sit on the cold hard ground I now look for that soft spot to sooth my tired muscles. That leads me to my tip.
Carry your soft spot with you!
In my pack I carry an air filled, ultralight, camping pad....