I've shot roosters, but only because they were roosting WAY high in the trees at night, and basically hard to catch, I use a .22 "CB Long" which is a quieter ammo made by CCI, I shoot through the heart/lung area. Nice large target, the bullets are round nosed so they don't create a lot of damage, just pass on (or mostly) through, making things leak in there. The rooster kinda trots a few steps, lies down because he doesn't feel too good, and dies.
If you can catch the roo, hanging or using a killing cone is good, hanging them by their legs makes them calm down it seems, but if you can't, and feel shooting is your best option, I think my method is a good one. You STILL have to be careful of your backstop, and it's still not very legal, but my neighbor and I are always putting down possums etc so the sound of a quiet .22 doesn't bother the neighbors.