One of the available diplomatic option is Educate child, what is important but often underestimate by the players. On the type of the child's mentor depends most of his abilities, traits and career. Part of child's statistics isn't conditional upon succession but upon his and his mentor's choices.
Your character can be both: if he's a child he needs a proper mentor, and when he is an adult ruler, he can educate young persons.
When the child is six, you need to choose him a mentor. If you don't many vassals will volunteer to do that, and be offended when you decline such a proposal. That's why solve the matter of education by yourself. During choosing the teacher, look at his abilities (they should be the highest possible). It's often important to choose wisely: princess doesn't need mentor-warrior and the young prince should be educated by the talented diplomats, stewards or intriguers.
Not without meaning are also traits and possibilities of career: there is a chance, that they'll be passed during the education. That's why it's very important to get to know their meaning and effects (Characters: Traits). When you're child's mentor, you can shape his personality, by choosing the proper dialogue options (screen above). Nevertheless, if you don't have high features it's better to give a child to someone more qualified.