As turbo said - You can get 10/22s to run subsonic ammunition. And most of the typical HV ammunition will actually be subsonic out of the shorter barrels. BUT whatever ammunition you use, it will seem pretty loud because you won't get a full powder burn inside the short barrel.
Also, your ammunition's terminal performance will drop with the reduced muzzle velocity from the shorter barrel. This might matter for hunting purposes.
Another fairly short option will be to take a Mare's Leg lever action (13" barrel) and put a full buttstock on it. No detachable magazine, of course, but would be a sweet shooter with peep sights on it.
Also, your ammunition's terminal performance will drop with the reduced muzzle velocity from the shorter barrel. This might matter for hunting purposes.
Another fairly short option will be to take a Mare's Leg lever action (13" barrel) and put a full buttstock on it. No detachable magazine, of course, but would be a sweet shooter with peep sights on it.