The Beretta M-71 is what you seek. You can still find surplus guns but the have pinned fake suppressers to get them imported from Israel. Spare magazines are $$$. The Mossad used this weapon but it’s in .22 long rifle, not .22 short. What they did was down loaded the cartridge for when the didn’t use the suppresser, because it made the package too large for practicality.
You can get a good substitute, now available commercially from CCI, the quiet .22 semi-auto.
It has a 45 grain bullet at 835 fps. It would cycle my TX22 fairly reliably, probably moreso with a suppressor attached.
The TX22 is maybe a little bigger than the M-71, but holds 16 rounds in the magazine.
It is about the same weight at the M-71 without the fake suppressor, 17 ounces.