They don't make them anymore, but you can still find the High Standard Double action derringer in .22 long rifle and .22mag. I used to have a .22 long rifle, but let it get away, a few years back. However, I recently purchased a .22 mag that showed up at a local gunshop a few days ago.
In a derringer, I can whole heartedly recomend the little High Standard, .22 mag. It is pretty compact, can be shot well with a little practice and the .22 mag does pack a bit of a wallop, of course it is loud, but maybe that isn't all that bad either. The barrels usually print a couple of inches apart, My bottom barrel is dead on, after I got a little used to it. the top barrel is 2 inches higher. I time my gun to shoot the bottom barrel first, and I was shooting it tonight and I am not kidding, I was able to shoot 1 inch groups with it at about 4 to 5 yards. Of course I had two different groups with one being 2 inches higher then the other, while using the same aiming point.
It is eaiser to shoot then those mini-revolvers, for sure, and to be honest, the bigger caliber derringers are often harded to shoot accurately, and they get too big for what they are pretty quick.