Hm, would be interesting what minimum energy a pellet rifle should have, but somewhere in another thread someone planned to use a .17 air pistol. Don't remember how that worked out.
I used a .22lr pistol a way back, definitly overkill, but there was quite some bloodshot meat in the neck area. Bopping works ok, and I always keep that as fast backup method if something goes wrong, but I built a spring captive bolt gun last year, and now that's my method of choice.
Only for rabbits that would freak out when being held I'm going to use my .22, 40J PCP pellet air rifle (overkill, again :roll
, at minimum distance for the scope (about 4-5m)
As for pellets, I would prefer the heavier ones, with better penetration. Hollow point imho doesn't work at this energies anyway, the point of an expanding bullet would be to slow the bullet faster and creat a big wound channel in soft tissue, and reduce penetration. Ok for supersonic rifle rounds on big game, but here you just want to punch a neat hole through the skull, and if possible all the way through.