FWIW, they are soft-bodied creatures in the same weight class as humans. However, you may end up with stem-to-stern penetration opportunities. Something that could penetrate full length and break stuff going out would be optimum. For a semi rifle, I'd want to step it up to 6.8 or 7.62x39 if the option to choose ahead of time was available. A 1301 Tactical or Benelli full of #1FC or well-patterned 00 would be next in line. Lots of chances with 9mm would be last, but I'd put it ahead of fewer chances. The choice between them depending on what's practical/acceptable to have with you where you are, doing what you're doing, as always.
I think the hard thing would be putting rounds in the right place fast enough, as cats' speed, quickness and violence of attack makes the fastest humans seem cartoonishly slow. Number of chances and rate of follow-up shots could matter a lot.
Second what Rob said about ambush predators. They are looking for a meal, not a fight. The only mountain lion fatality I have any familiarity with was a guy who separated from his group to relieve himself. Cat attacked while he was "indisposed," crouching down and distracted... Not standing his ground in a ready position.