I believe all air rifles are a firearm under Federal law... those over 495 fps require a PAL.
If used illegally, I believe this is the case.
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To the question (assuming it's safe, legal, and you have your landlord's permission) the two main considerations for airgun noise are;
1. The sound of the gun itself
2. The sound of the projectile making contact
CO2, and pneumatic guns are the loudest...and should probably be ruled-out if noise is the main concern. At the other end of the spectrum, spring piston guns. These can be as toy-like as a Daisy Buck BB gun, all the way up to PAL rated magnums. The more power=the more report. A human sneeze is probably 3X louder than a Daisy Buck. lol As for targets/impact sound...start thinking "Cardboard box filled with old, folded towels/rags" and go from there. The more power/the more filling required so the projectiles don't go through. Not going to describe this in detail, but use your imagination. Not complicated, and it works.
Airsoft is another option, the non-battery-powered/spring guns can be quiet/fun. At the ranges you're probably using them indoors...not a ton of difference probably. Certainly, if you're comparing to a spring BB gun.
At the end of the day, there is risk...it is a bit messy, and you need to be doubly-aware of your backstop. Not a great idea overall, maybe less so when you rule-out allot of the "cooler" cheap/fun airguns in the interest of keeping quiet.