Snares, very effective but need placing and setting properly.
Always set them on the rabbits "run" or its "pad"... rabbits use those as their "motorways" so to speak.
Snares need frequent checking, at least 3 times daily so for me setting snares is a weekend activity.
.177 rimfire rifle wont destroy a carcase and it is quite usable if its shot with one of those, I regularly use a .22 rimfire rifle to hunt rabbits, a clean head shot is possible up to 50 metres away... and up to 100 metres with a .177 as the round is much flatter and of a higher velocity.
The trouble I have is that the rabbit population has been destroyed by foxes, although there is more now that we have been proactive with fox control over the last couple years.