At one time, shorts were cheaper than Long Rifle, by a fair bit.
Not so much any more.
My advice, buy a 22 LR and shoot Remington Subsonics, if you want the low noise level. Or CB longs. Heck, you CAN shoot shorts in about any 22, accuracy is not optimum though.
22 Short rifles used to be made with a 20 inch twist rate, LR uses a 16 inch twist, mostly.
Soooo... Choices..... Want a Short chambered rifle, you are looking at old stuff pretty much. Browning used to chamber their Semi-Auto in 22 Short. Not cheap. Pretty much meant as a Shooting Gallery gun. May still be available. Winchester Low-Walls and Winder Rifles were sold for the Short cartridge. There was some serious competition carried out with them at one time. Again, not gonna be cheap.
Any more or less 'modern' bolt action single shot, as well as a pile of repeaters will handle shorts, but whether the accuracy is there, I can not tell you off-hand. May be satisfactory for your needs.
Finding a rifle made these days, barrelled and chambered only for Short ammo. Good luck! I think you are looking for something nobody thinks is worth making in the modern market.
Cheers
Trev