.22 air rifles would probably work.
Dacula (city of) is in Gwinnett county and Gwinnett has the same prohibitions on air guns as on real firearms.
Aguila makes a very quiet .22 round. Something around 750 fps at muzzle. Sounds like an air gun, but close in deadly. I’d not use it on a fox, however, as I am, in the end, pro-fox.