It varies from mod to mod. In the Smurfs mafia, I gave the option to the Godfather that he could choose someone else to perform the kill. But with a catch though. That person could not perform their own night role (if they had one).
Think Pokemon mafia had the same rule. Can't remember though.
That would be my understanding - that if they had another night role, they would lose it for that night. Which is why the godfather would tend to share the role mainly with 'goons'.