I would recommend cervical dislocation. It's easier for one who has to do it on their own, and you don't have to have a stump or "make" anything.
1. Hold the chicken's feet in your right hand so that its breast, neck, and head are resting on the ground.
2. Place a broomstick (rake or shovel- whatever) over the back of its neck.
3. Now you step on both sides of the stick (pinning down its neck) and at the same time pull up firmly on his/her feet.
The bird will likely flap around a bunch, but it is as dead as if the head had been cut off- in fact often the head does come off.
Sorry if this sounds graphic, these things are hard to do but sometimes necessary- I feel its best to be really explicit. The clearer you are on the process, the less stress for you and less stress/pain for the bird.
Good luck!