I've gotten one with a .410 out of a Rossi brawler, but it was pretty close. The pattern on those is not good past just a few yards ( < 4). That said, it was lucky, and I wouldn't recommend it, and if I had the shot again I wouldn't take it (we patterned the gun after taking the grouse, and realized it was a lucky hit).
I then bought a .22 Ruger Wrangler, but I can't get it to hit anything, so still need to try some better ammo. (I can hit anything else just fine with my other pistols).
If I could do it all over, I'd spend the extra money for a nice semi-auto hunting .22, and absolutely put an optic on it. After-all, we only want to take the best ethical shots. Seeing a wounded bird get away is the worst.