Here's an article about Black powder 22's, looks like they were about 1100 or so fps.
Looks like the 1100 FPS value was achieved in a rifle with a 40 GN projectile. Match grade .22 LR ammo with the same weight projectile achieves velocities in the 1050 to 1080 FPS range with a 28 inch barrel. CCI SV LR may work just fine.
Stay away from stingers or HV ammo. Try the drop in chamber test with a LR.
Ammunition is like firewood. The more you have, the warmer you feel.