Can you change your succession law to one that allows you to pick a successor? If so, this would be IMO the easiest and best solution.
Feudal elective would probably be the easiest for you, although there are many others. Eg: Tanistry (requires Celtic culture); Muslim Open (by converting to Islam); access to the "Meritocracy" feature (eg. by converting to Buddhism).
If you're really desperate, consider Elective Gavelkind. Yes, you lose land on succession, but at least you can pick your successor. (Pick a young one, so it's easier to change back.)
If you're really
really desperate and don't want any of the above, Seniority is an option. (The main problem with seniority is that your rulers are old when they succeed. This has many disadvantages, including the fact that it's hard to stay in power for the 10 years necessary to change the succession law to something else.)
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You may be able to disinherit him, for example:
- Imprisonment (see below for some ideas) + send to holy order (only if a holy order of your religion exists - eg. Templars, Hospitallers)
- Imprisonment (see below for some ideas) + order to take the vows (requires SoA DLC and a monastic religion)
- Make him a bishop (may not be possible if he's heir to a title; I think you'll need to personally own a church and give it to him as his first title)
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If you still want to solve the problem with murder then, mostly, the only way is to imprison your son then execute him. This will always give you the bad "kinslayer" trait, but maybe it's worth it for you.
- If he's in your realm then you can try to directly imprison him, without a reason - but this is not certain (he may flee) and both the imprisonment and execution will give tyranny.
- If he's a child and you siege down the castle where he's living (eg. by provoking a war with his family) then you have a small chance to imprison him. (It seems to be very rare that you imprison adult men after a siege.)
- If you wait until he's an adult and excommunicate him then:
- If he's in your realm then you can imprison him and execute him without tyranny. But the imprisonment is not certain (he might flee).
- If you excommunicate him then give him a title, you can imprison/release/imprison/release without tyranny until he revolts; then win the war; then execute him without tyranny. This is certain, but requires a lot of steps! This is the imprisonment/execution option I would pick.
Duelling is another choice, but in all cases: it's risky (you might not win); you will get "kinslayer"; and if you deliberately kill him after winning then you will also get "merciless".
- Become zealous, excommunicate him, take the "war" focus (Way of Life DLC), then duel him (excommunication is a valid reason), hope you win, and kill him at the end. However: he might refuse the duel (eg. if he's craven).
- If you antagonise him (using the red button just right of centre in his character screen), he might eventually challenge you to a duel. However, I don't have the patience for this - I find it too unpredictable.
- If you antagonise him and he becomes your rival (requires several years of antagonising) and you take the war focus, you can challenge him to a duel. However: he might refuse the duel (eg. if he's craven).
- If you educate him using the education system from Conclave DLC, you will have the option to make him an ambitious rival at age 14. Wait til 16, take the war focus, duel, etc.
Other random options:
- If you have access to a Great Work with a feature that permits "Private Conversations" then you can invite him to a conversation and try to kill him. However: he may refuse the invitation (eg. if he dislikes you); he may win the fight (you die!); and you get "kinslayer". This is IMO the best option overall if you have the GW and are a much better fighter and he likes you.
