Killed my first coyote with a 30/06 loaded with 110 gr SP. I bet your 308 loaded with 110 Barnes ttsx would work for coyotes and 99% of the deer you hunt too. I've never owned one since I'm hung up on other cartridges, but how can you beat a .204 if you are just starting out? I use a .221 Fireball an awful lot for a calling rifle and it is about ideal balance between noise, accuracy, and anchoring ability.
Another consideration- All the bigger rifles make so much noise they ruin multiple call-in opportunities the quieter rifles, like the .17 Hornet, leave open. That can be a huge factor in a days success ratio.
