If I was in that situation and had a choice, I would choose guillotine, or firing squad, or there is a form of liquid cyanide that is reported to kill effectively in about 15 seconds. (In the book about The Iceman, and I think that was the name of the book.)
Since taking your own life is a sin, my idea is to create a death row cell where the inmate can take his own life. It would look like this.
The cell looks like an ordinary death row cell. However on the wall there is a “push to fire bullet” mechanism, not unlike those break glass to activate alarm devices. There are two hand prints on the wall and two foot prints on the floor.
In order to activate the firing mechanism, a five point circuit needs to be made. The feet go in the foot print, the hands go in the hand print and the final connection is the head touching the activation button. This is the only way the bullet can be fired into the brain. It’s all biometric so only the convict can activate it.
It’s cheap, it’s quick and it is emotionally painful to the convict. Having to sit there day after day looking at this device would drive someone mad. A fitting end.