I don't know.
In fairness it would depend on how much time there was left until they were to be put to death. If they've exhausted their appeals and death-by execution is around the corner, I'd be tempted to have them wait. The problem there of course is that if they are suffering from a terminal illness, they'd likely have medications which would diminish the usual power associated with watching a person get their lethal injection, facing the firing squad, attend their hanging, being gassed or being electrocuted.
So is it fair to make them wait until the very end or should an alternative be offered? Well, a solution would be to have them sign a waiver allowing the death penalty to administrated immediately, refusing any further appeal. Additionally, whatever method of execution was going to be used, must still be used. So, yes, in a sense, I would allow them that right, it just won't be carried forth in the same way as it would be for a non-inmate.