Nitrogen asphyxiation should be effective and painless, but not if the person fights it. Which means it'll be hard to use as an execution method (unless you surprise them with it somehow)
You could give them a sedative. They pass out and can't hold their breath, then you administer nitrogen. You could probably even find an acceptable oral medication so you wouldn't require a doctor to administer it. I'm in no way saying this is acceptable, but it isn't that difficult.
Put them in a small sealed room with airflow you control. Using a randomly generated number to pick the start time (within some maximum that's deemed appropriate), you then throttle up the nitrogen and throttle down the oxygen.
The time spent in the room would still be pretty terrifying so I doubt it'd be much better than the mask... Maybe the room is their cell and it's a randomly chosen day within an execution "week" where you make sure they're asleep first?
Probably best just to not kill people of course, but if you're gonna do it, do it the most humane way possible.