Ray,
Those were taken with a Condor .22 & .25. But this winter I took a couple of possums with the 350 .22 which are a little tougher (their skulls) than a raccoon. I used the JSB Exact Jumbo 15.8gr pellet (domed). You can't go any heavier than that or the spring will start losing its properties (power). The gun is slightly detuned so it shoots them around 780-785fps (about 21fpe), compared to 805-810fps with my old 350 .22 which was factory stock. You can also take them with other good domed pellets like the CP or CPHP because they are hardened with antimony (yeah all the bad metals for your health) and penetrate amazingly well, or the Predator but at 30yds I 'd stick with a domed pellet, not a hollow point. Avoid hollow points beyond 25yds. My 350 is most accurate with the JSB Jumbos and 2nd are Superdomes which are also good. The possums were 23yds out.
I have taken many Groundhogs/woodchucks with the 350 .22. Several were from 30 to 43yds out. Some if not most of these Groundhogs were bigger and heavier than any possum which averages 8lbs. The CP's, JSB Jumbos, and Kodiaks I was using went through the Groundhogs' head every time no matter what the distance. On a stock 350 14.x pellets like CP, CPHP & Superdome go 835-850+fps. You don't really need any more power than that. The 350 will take any small-game creature inside 35yds no matter how big it is with a good head shot. It can deliver 13-14fpe @ 50yds with a 14.3gr CP. You only need 10-11fpe on impact for a quick kill on a coon or possum (and 8-9fpe on Groundhog), but the more the better.
If you can afford a PCP (Disco, Marauder, Condor, etc.) I 'd suggest you go with that because at 30yds you want to make sure the head-shot is nearly perfect. The 350 can be a little rough around the edges when it is stock and not tuned, but I took many Groundhogs with my 1st/stock 350. You really want to make sure you can get 0.5" groups at the distance you plan on shooting a medium-sized critter. Most Magnum Springers will not give you good groups like that out of the box. To me 1" groups are not acceptable to go after big critters. The more accurate your gun, the more your chances are of dropping the animal instantly and recovering it. Magnum Springers should really be tuned if you want decent accuracy, whereas PCP's do it out of the box and better.
Here are a couple of possums I took with the 350 .22 this winter. One was a frontal shot and one broadside. You can see the POI. I will not post the dozen Groundhog kills I have with the 350 .22 (with gun in the pic) because the possum has a harder skull than most, so to me it sort of is the ultimate quarry (w/coon a close 2nd) for a Springer @ 30yds or beyond after a fox or coyote.