The thing is, "centre mass" ain't gonna kill with any sort of consistency with an airgun of any power - you need to be getting either head(brain/stem) or heart/lung. Shoot anything in the guts and it'll just crawl off to die slowly...

Personally for ratting I rate something fast cycling - had great results with a Steyr LP5 in carbine format, taken hundreds with an AA410k as well, but now favouring either a pump-action Skan or martini-actioned Phoenix

Points taken about headshots being tricky, but at close range you should be well able to get the shot into the critical spot