I find shooting them in the back of the head with an air pistol, just about between the eyes and the ears works as a stunner if not outright kill. First one I did, I dissected the head to check I'd got the right spot and found the pellet had gone right through the brain. I follow this by cutting the throat and allowing them to bleed out, but I imagine breaking the neck and bleeding into the gap would be equally as effective and a lot less messy!
Stunning, even if only with a short plank or hammer, is essential before slitting their throats: the brain stays active for a significant time after. I used to decapitate birds, which is ultimately the same thing, but it is VERY unpleasant holding a bodiless head and feeling it moving eyes and beak in your hand!!