Never seen a cougar killed animal in a tree - or heard of anyone who has. They cover up their kill as soon as possible after dragging it to a safe location.
A few years back I surprised a cat while walking back to camp at dusk. All I had to do was release my arrow to get it while it was growling at me 12 feet away.
But it was a female with a yearling cub so I didn't shoot. Next day I went back and found a cow elk she had killed - buried under some brush. I took the cows jaw bone to remind me of the event.
Cougars won't put a dent in a coyote population, but wolfs sure will.