Finding a rifle cartridge that can be loaded in a single-shot pistol to shoot 200-300 yards is not all that difficult, depending on what you want it to be capable of, at that distance. Check out the JDJ line of cartridges as well as the work done by Gary Reeder...both make a good array of very powerful rounds, specifically for hunting with a pistol. Another resource who has done quite a bit of work along these lines, and is easier to work with, in my opinion, is Mike Bellm. His 309Bellm round might be just the thing you're looking for and if it's still not quite powerful enough, he'll be able to point you in the right direction.
Keep in mind that the actions most often used for this kind of shooting, the Encore and Contender/G2, benefit from a rimmed case, so many of the traditional rifle cartridges can be used but you're better off with something that has a rim, for headspace. A good example would be choosing a 307 Winchester (rimmed) instead of a 308. You'll also want a good grip and forearm along with a ported muzzle or brake, because handguns capable of that kind of performance can be tough to control, without those improvements.