Check the files in \common\council_positions\.
I do not understand everything there but it seems that for loyalists you want content, trusting people, from your dynasty or even better close relatives, friends and/or lovers is a bonus too, as well as having an opinion of you above 95 but never envious ones.
Traits that add to the possibility of picking any of the other four - cynical, craven, just, paranoid, brave, honest, proud, zealous, humble, envious, ambitious, etc. etc with percentages of your troops/realm size vs. his troops/realm size used in the calculations as well.
Basically go homo seducer, make a bunch of lovers (preferably close kin) with appropriate traits and you'll have the perfect council.