I'm sort of surprised no one's responded to this yet. Sorry ArrisBoch.
Anyway, I think there are a couple of routes you could go. It could be some kind of divination item, allowing the wearer to Know Alignment or Detect Thoughts at will perhaps. Or it could be a buffing item, raising one or two attributes (definitely Wisdom, and also maybe Charisma) ensuring that he or she who wears the crown will rule justly and wisely, regardless of who they were before their royal ascension. Perhaps the kingdom is especially pious towards a given pantheon or god (divine right of kings?) and the crown allows them to commune with their god or gods. Or a favorite of mine: the crown absorbs a bit of the memory, skills, and personality of the kings who have worn it before, providing skill bonuses, possible Int. buff, sage knowledge, etc. Or depending on how artifacty you want to go, any or all of the above.
(Artifacty? Artifacty? Curse you Buffy!)