There are few dedicated rimfire scopes as "rimfire" has a bit of variation too.....50 yds is not always the focal length and the ones you can adjust to your rifle give you a better option. In the budget range (without going to cheap sh_t) would be the Nikko Stirling Mountmaster AO and the Nikk Airking AO. The Airkings are the better of the two and are a bit more pricey but at around $200 for a 3-9x40 still pretty good value. The AO mount master is closer to $140.
There are better ones, and whether you get a side or front focus, both are fine for 22s. For a rimfire scope without the AO you start looking at Nikon, Leupold and others and these can start to approach better quality as well as higher prices and from my experience the Nikko's perform very well.
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