I have had mild nitrogen narcosis while scuba diving at 120’. It was rather pleasant. If they're looking for a humane way to kill somebody they could do worse.
1 atm N2 sounds straightforward for this and relatively cheap, although not as cheap as a noose, a bullet, the guillotine, or the chair. Just be careful not to off the good guys. Lock perp alone in room with big screen tv playing his choice and a chair. Flood room with N2 without warning. Vent it safely after 10 minutes. No attendants needed, just gas concentration sensors.
Now, if I can believe Tom Clancy and his 'John Clark,' hyperbaric N2, with variable pressure and enough added O2 to sustain life, is much less humane. Certainly 'the bends' is real and can cause painful chronic damage. I just don't know whether it can be induced as brutally as Clancy wrote it for a deserving perp. I forget in which of his books, this occurred, but the scene was memorable.