You should try to boost your influence one way or another (conquest, relieving beseiged allies, crusades(doesn't apply to danes though), defeating rebels, most often just conquest) I believe the higher your king's influence the more likely your sons will get good stars. If you want you can ferment rebellions and have your royals quell them to gain stars.

Be sure to build things to get the builder virtue and the steward line of virtues is good too (building farms) Those increase loyalty and loyalty and happiness which'll help offset the low influence.