I find that JSB or Haendler & Natermann (H&N) pellets work well in all of the air guns that I've used. Try the ones that weigh between 14.66 to 18.13 grains. Also, the Air Arms Diabolo Field in any caliber work pretty well in most guns.
Then you have slugs, which are not your typical pellet shape. But, more bullet-like. These can be very long and may require you to hand-load then one at a time. however, they are devastating on pests!
Happy air gunning,
Mondo