I've recently done the exactly same thing as the OP. I shoot bullseye but need more practice when I'm not at the range.
Here are the air pistols I found that could do rapid fire. Some of them are quite expensive (more than my target 22!)
Drulov DU-10 Condor
IZH 46 - very accurate and good entry level single shot.
And there's a third option: Gas-blowback airsoft pistols. Don't laugh too hard. These things are full metal now, with reciprocating slides and operate just like the real thing, down to the safety and slide release. They have recoil that is just a little less than a 22 but does disturb your sight picture so you have to do recovery. They are actually fairly accurate and fire at 300fps which is not all that much slower than a CO2 pellet gun. The triggers are actually not bad, a little creep but about a 3lb break. Plus you can shoot them indoors.
Finally, you can use a laser bore-sight in your gun when you dry fire. This helps to be able to see if you are pulling the trigger straight back or not by watching if the laser dot moves. I've found this very helpful in diagnosing problems in my trigger pull.
Target-talk is the place to go for bullseye. That or there is a lava list also.