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.
If you're lucky enough to be on private land and can leave your stand up during the off season you can tie an old piece of cloth or something of the sort to your stand. I like to use an old camo bandana that I have. That way the deer get used to the movement and eventually don't bother even looking up when there is slight movement. This may just give you the time to draw your bow or raise your gun without being detected.