Umm, there's a few funny notions rolling around in here, including the premise of the thread. However, I can share some experiences that are perhaps relevant, but are a small sample.
I'm a professional forester and spent the first 12 years of my career working alone in the woods several days a week. The last three years that aspect of my life has greatly diminished due to "advancement" but I still go to the woods alone for work, and recreation both. I've actually had a lot of interesting animal encounters when I think about it.
Bobcats, coyotes, and mountain lions are prevalent where I live. Bear wander in now and then, and the occasional wolf, but the state typically removes them as they tend to cater to local ranchers pretty heavily. Of those three, bobcats are the least concerning to me. A few years ago I was scaling a deck of post and pole material to be sold, and while tagging and measuring the deck a bobcat came crawling out about four feet from me. It wanted nothing to do with me, and simply crawled back into the pile to get away. It was cute more than anything. When snow drops you can see the repeated cat tracks in the snow as they do their daily checks of the small log decks for bunnies to eat. Granted, if one was rabid, or you cornered one somehow, it could be a problem. However a BIG bobcat, and I mean real big, runs in the neighborhood of like 40 lbs. The only way a 9mm wouldn't stop it was if you were throwing the bullets at the cat rather than shooting them.
Coyotes can be a little more hazardous, though every time I've seen them they were trying to get away from me with one exception. I was GPSing a timber sale unit when one came out of the bushes about 40 yards away. It turned, saw me, and charged. When it was about 20 yards away it must have realized I was way bigger than it initially realized, because it veered away into some other bushes and ran off. This was late spring, so I'm guessing it had pups nearby and was trying to chase me off, or lure me away from them. I've literally walked up on them dozens of times, including surprising one that was stalking a few deer that had a fawn in tow. They can be dangerous, particularly where they become unafraid of human habitation, or start to see human homes as a food source (garbage). There have also been instances of coyotes hunting in small packs. One tactic that has been observed is that an individual will approach an unleashed dog and attempt to play (play bow and other typical canine play activity). Then they get the domestic dog to follow back to where another coyote or two are waiting, and when they are in striking distance, they kill and eat the domestic dog. I've heard of a few instances locally of this happening where the dog owner looks out the window to see a coyote interacting with their dog. They run outside to stop it, and the coyote runs off. Unfortunately the dog follows because it's in play mode and not really listening to the owner. Children are at risk as well, illustrated by the video above. All that being said, 99% of the time they will run off if you encounter them in the woods. If they don't, a BIG coyote is maybe 40 lbs also, with an absolutely enormous one coming in at maybe 55 lbs. A 9mm loaded with quality ammo is going to be more than enough to stop one.
Honestly, a 22 Mag is probably plenty to stop either animal. In fact I'd say a 9mm is ideal for coyotes, as you are more likely to be carrying more ammo, and several small targets may be hard to hit. Misses could be a factor.
I see some mentions of 357 and 10mm. Well, if the notion is that you are better going with overkill, I get it. Also, if there are larger critters, like black bear or lions about, those cartridges are good choices as they will be perfectly adequate for all those animals. Though the behaviors of these animals are all different. If you've never been around lions, they make life spooky at times. If you've never seen one running, let me tell you that the word "speed" takes on a new meaning.
However, the original question was about 9mm being adequate for bobcats and coyotes, and the answer is yes. With a good bullet it's more than adequate.
I was actually charged by a fox in my driveway one night after walking home from the bar. It got within 8 feet of me. It ran off when I burst out laughing at its show of force. Back arched, hair bristled, sideways bounding motion to make it seem bigger...……. Pretty cute and funny to watch. It got an A for effort.