Nitrogen asphyxiation is probably the gentlest and most comfortable method of executing someone I can think of.
There's a funny quirk of human physiology: we don't have a mechanism for feeling hungry for oxygen. The desperate and painful sensation of needing to breathe fresh air? That's your need to expel CO2. Cinching a Hefty bag (not sponsored) around your neck is a miserable experience because you're poisoning yourself with your own carbon dioxide. Let the bag leak around your neck, and inflate it with a constant supply of inert gas - like helium, or argon, or nitrogen - and you won't notice yourself dying. I recommend helium; it'll make your last words that much more hilarious.
Reason I know this: I'm a flight instructor; you want to go somewhere where there's not enough oxygen? Get in a plane and go about 30,000 feet straight up. You don't feel that panicky "I can't breathe" sensation up there because you can freely exhale CO2, but there's not enough oxygen to keep your body working for long.
It is my understanding that among the states that still practice the death penalty, the methods that the law authorizes are lethal injection, electric chair, cyanide gas, hanging and firing squad, and the last two are technicalities that haven't been repealed yet. Compared to these methods, inert gas hypoxia is a lot more comfy. The electric chair and cyanide gas are proper horrifying, lethal injection is supposed to be humane on the theory that they anesthetize you before chemically stopping your heart...except no actual anesthesiologist wants anything to do with it, so they get some random guy to do it and they pretty much always botch it. It's not hard to flood a room with nitrogen, though.
The cruelty in this subject is found in these particular states executing people often enough to worry about it.