They are not particularly hard to kill. The best cat hunter I knew used a revolver in 22 mag, right behind the ear, not something I'd try, but he is a crack shot with the thing, passes marginal shots and hunted cats all the time. So if you are confident hitting a relatively small spot on a treed cat with a pistol, I'd guess any reasonably powerful legal cartridge will do with a fast quick expanding bullet in the lungs, or a heavy cartridge 41 mag+ loaded with about anything. They can sit at odd angles and be obscured by branches, so we've all used rifles on them, 357 mag or more. I have a Marlin 1894C in 38/357 I'd use, with the 357 mag flex tip bullets, about as light as I'd go. I killed mine with the ever handy lever action 30/30.
There are times they won't tree, or even if treed, the shot is longer or more difficult than you planned for. So my advice, if you are only going to hunt them rarely, would be to use a rifle, unless you are an expert with a pistol. Or at least have a buddy carry a rifle for you in case the pistol you have seems not the tool at the time. You do want a quick kill for the sake of the cat and the dogs.
My friend did have one come at him, he had his 22 mag, it is not a cat stopper, cat chewed on his foot so he was able to head shoot it. It was a young tom, he was very lucky. But he kept carrying the 22 mag after, go figure. I had one come at me, speed of light, they are fast, 30/30 dropped him less than 2 feet from me, I was very happy to have the power of a 30/30 that day... So while it is very very rare to have an issue with a cat, some of them can make things very western in a heart beat or less.