If you're going to eat it I don't think you want to put opiates in the bloodstream, do you?
The best advice I can give you, whatever method you use, is to hold the bird upside down for a minute or two. Blood rushes to the brain and sedates the bird. My DH and I use the broomstick method for dispatching a sick or injured bird this way, usually there is a little flapping afterward but the bird is definitely dead as he pulls hard enough to decapitate to be sure, the flapping is just reflexive. (If we're going to eat the bird we take it to a professional. We're no good at eviscerating and plucking.)