RE: Mountain lions, in PA or NY?
NYMAD1
.17 HMR should do in a coyote with good shot placement but, I wouldn't be trying any shots over about 100 yrds.
I have killed yotes with a .22 LR with a head shot at 50 or so yrds. and I shot one at 20 yards through the front shoulder with a 12 gauge 3" Federal Slug and that one didn't even act like I hit it. I thought I missed untill I walked over and found the blood trail. That was a pretty big dog though he has about 60lbs. I tracked him 150 yrds into a swamp befor I found him dead.
I guess it depends on the animal. I haven't had to track any that I've taken with my .243 though. I have only needed a second shot a couple of times and that was because the first shot was a bad hit. I can count on my rig for shots out to about 350 yrds though. I've got a Bushnell 6 x 18 power scope and a harris bipod on a Savage model 11 .243 Win Mag. I don't miss often.
If you give the .17 a try let me know how it works out for you. I have been thinking of getting one for my daughter. She is getting into hunting now and has a .22 but we I'd like to get her into the higher power rifles she likes shooting and is getting good at it.