G'day,
It must be remembered that air rifle shooters in the UK are limited to power out-put of 12 ft. pds. or under using tuned break-barrel air rifles unless they have a Fire Arms Certificate [FAC], yet routinely head-shoot rabbits at distances out to 30 yards or so. The point is that great power is not necessary for rabbiting. The modern PCP rifles are clearly very accurate, but there is the issue of pressurising them either by stirrup pump or compressor. I have an acquaintance who is shooting rabbits out to 60 yards with a PCP which I can only describe as more like a cannon - it's massively powerful - too powerful for your planned use. I have a number of Weihrauch break barrel rifles of which the HW 80 [in .177] is exceptional as is the HW 50, but there are other Weihrauch models that would meet your rabbiting needs. A calibre of .177 is more than enough, but there are heavier calibres. For use in the back yard air rifles still make a noise, often quite loud if their power output is very high. That's where sound moderators/'silencers'
might be useful in your case if legal:
https://www.airguninsight.com/air-gun-s ... d-to-know/Break barrel air rifles take a bit of effort to master in terms of accuracy as they have a double recoil, but they would be my choice in your situation because of their simplicity. As for ricochet light-weight air rifle pellets
do deflect easily so having a safe and soft back-stop is mandatory.
Airgun Nation is a good source of information:
https://www.airgunnation.com/Jim