.22LR RIMFIRE SEMI-AUTO
I am pleased to see you already have a .22LR bolt-action rifle, as this will always be more accurate than a semi-auto, though many modern semi-autos are good and offer a quick second shot — handy when lamping rabbits and second or third shots have to be taken in quick succession.
The obvious choice would be a Ruger 10/22 rifle, as this is the industry standard.
It is available in many guises — from basic, plain Sporter to target-grade models — with stainless steel finishes and a choice of laminate, synthetic or walnut stock.
There is also a vast range of accessories to accompany it, such as scope mounts, spare magazines, upgrade kits for triggers, new stocks, and even fluted target barrels.
Viking Arms is the distributor, but most gunshops will stock at least one 10/22.
The Remington 597 semi-auto is also a good rifle.
It is well-made, accurate and reliable with the correct ammunition.
The 597 is also available in many configurations, and the synthetic stock version is particularly practical for pest control.