Quote Originally Posted by elbasto
Assessinate him.

You could also send him to fight a suicide mission but make sure you unmount him first so that he can't run away...

Also high influence seems to affect the quality of the heirs. Not inmediatly, but I've seen it work in 2 or 3 generations. To use this, winning a couple (usually two are more than enough) of crusades or lifting your an ally's siege can help.

When able, I try to keep a non catholic rebel province inside my empire. After my king dies y crusade to it, take it, fall back, rebels came in and retake it by crusade... I repeat this every time a new king is elected.
Also, sending spies to an ally's province to generate rebellions, you can lift your ally's siege as needed.
I rathe keep the good men since kings die with all their stars, but heirs die and their stats and transfered.