If your faction is very large -- I want to say the threshold is around 30-40 provinces -- it tends to get a lot harder to find princesses willing to marry into your faction, regardless of your king's influence.


There is a drastic measure you can try: You could deliberately kill off your king. Your crown prince would then probably marry a local noblewoman in a few years, and with any luck he would live long enough for his heir to take the throne himself.

Obviously, however, I don't really recommend this strategy unless you feel it's absolutely necessary.