A PCP .22 that can be tuned up to push the heavy 25 grain pellets at 800 ft/s would be sufficient, but that in my opinion is about minimum. A .25 PCP is easier to get the velocity to 840 to 880 ft/s with 25 to 33 grain pellet, which would be better. The slightly larger diameter makes a bit bigger wound channel, and is more likely to hit vital areas. The .25 will use more air than a .22 but for the few shots taken at critters like that filling should not be too much of a problem.
Oh, and keep your shots to a maximum of 60 yards. Pellets lose quite a bit of energy as you reach out. You might think that you could then push the pellet faster so that you do have down range energy, but the problem then becomes stability with the pellet and accuracy suffers tremendously. The velocity at which pellets go haywire is typically around 900 ft/s. Some guns can seem to do o.k. a bit faster while others somewhat slower.
Round nosed pellets do quite well on critters, and often better than the hollow points or the plastic tipped pellets. The possible exception is on smaller critters and closer where the expansion does not prevent adequate penetration to vital areas.