I will not choose a method because all options require a trained an licensed medical professional to implement humanely, and nobody who qualifies will participate because they have ethics that prohibit causing harm to be licensed medical professionals. That includes putting someone to death against their will.
Picking a method is agreeing with the assumption that we have to put people to death.
The thing is, all of the humane ways to kill someone require the person to be a willing participant in the process. Nitrogen works when the person is relaxed and breathing normally for example.