Rh,
Spot and stalk is a tough way to do the cougar thing. Shooting one out of a tree is a bunch different than having an unknown distance, angle, wind, etc.
I'd pick whatever rifle you would use for a yote sized animal but with a bullet that held together a bit to avoid severe hide damage. One of the solid copper bullets that sheds or not sheds its petals should work fine.
I've used the Lost River J-36 # 3200 fps on yotes at distances from 40 yds to way-out-there with great success in a 270 Win. Exit hole never any larger than a quarter when shot through the rib cage.
Good luck.