Craven, Slothful, Gluttonous, Content AND a lowest-rank education trait. I can scarcely imagine a worse heir without adding bad congenital traits...
Your heir cannot be intentionally removed from the line of succession by making him a bishop. As you have discovered you cannot plot against your offspring without Mods. Such mods DO exist though, so there's that.
Without Mods, there are a few dangerous councilor missions that could get him killed. I have often heard that using a Spymaster to steal technology from powerful rulers is principally a good way to get a dead Spymaster. Sending a Chaplain to convert Pagans will usually get them thrown in jail, which could easily lead to an early grave.
If you haven't changed your succession laws during the current Emperor's reign the guaranteed fix is to change the laws. From your screenshot, Ultimogeniture would give the kingdom to a younger brother who is yet a child, but a child ruler might still be better than Enrique the Idiot. Elective would give you the option to let you and your vassals choose your heir, surely somewhere in your family there is someone more fit to rule than Enrique the Idiot.
As a last gasp effort (due to the considerable costs) you can likely imprison and execute him, but that way lies some SEVERE penalties, a sizable amount of tyrrany penalty and Kinslayer Trait besides.
I can imprison and execute him though, which I'm now thinking is my only option.
– jellier Mar 11 '15 at 20:29