Also, build build build.... it helps if you can earn your king his 'great builder' and 'magnificent builder' stripes (+1 and +2 loyalty resp.)
Generally I find a degree of stack micromangement helps when things look dicey. Let low-loyalty units stand alone, and find the highest possible loyalty general to 'lead' whatever remains in province - the idea is to make rebellion suicidal for the rebels. Get real dodgy types close to the king ASAP.
I think Drone has covered everything else.
This is just the short-term measures, of course. Longer term, you need to keep an eye on your royal family, as you may need to prune the tree sometimes.... If you have a really useless looking heir it can help to send him on a one-way mission to bring up your second son as the new heir apparent. Also if you go through a string of brothers inheriting the throne (because sons are still too young), you can get through kings too quickly which seems to reduce your influence or at least reduce the time available to build up good traits.