Most painless methods have a high survival rate and might cause permanent disability

Nitrogen suffocation is the way to go. The body can't detect oxygen because it's using it, so we detect carbon dioxide to determine if we're running out of oxygen but we completely ignore nitrogen (which makes up like 70% of the air). Thus, if you suffocate on nitrogen you don't notice any carbon dioxide build up to trigger the suffocation response, you just start to feel the affects of a lack of oxygen and die in blissful hypoxia.

I'm pretty sure this is what they do in the little pods in Switzerland. We should also do this for livestock, in my opinion, as killing pigs with carbon dioxide is inhumane (they respond the same as people). However, the fact that nitrogen kills people so easily and sneakily makes it much more dangerous - nitrogen can expel all the oxygen out of the room, and people won't notice, so you need expensive equipment and measuress to prevent and detect leaks. Meanwhile, CO2 is heavier than air, so you can just have open pits of CO2 and lower pigs into them, and all you need to protect people with is a railing. However I think the meat would be better if the animal wasn't in agony as it died.

Fun fact: jumping is the single lest effective method of suicide. You are very likely to fuck yourself but not die, instead having to spend weeks in the hospital and possibly be disabled for life.