The main difference between a rimfire scope and a centrefire scope with most decent brands, is simply the focal length (Objective focus.) With scopes up to about 6 power (so you 4x is included) it wont make a great deal of difference. The issue of parallax really only causes issues as you get higher magnifications at closer ranges.EG 9x at something 40 metres away. Rimfire I would suggest either a AO scope or a rimfire dedicated scope but for rabbits out to 100m as you stated, I would suggest a mil dot or graduated reticle of some sort would be a bigger assistance. My bunny rifle has a Nikko Stirling Air King 4-12. These are usually around the $200 mark and they work very well. I could spend much more on a scope, but with the accuracy I am getting, it would not make a noticeable difference.
And for reference, in case anyone is wondering, Air guns are far more savage on scopes than a rifle. Those springs rattle and shake / vibrate the hell out of scopes.
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