Princess Maker 1

The feature in which you may visit the castle and raise your popularity until you can meet the King was started in PM1!  As your daughter gets older, she can meet more of the people in the castle, and I believe Courtesy classes also help.

I haven't met the King yet, but I have met these people in this order:

Guard     Captain    Chamberlain   King

I do know that the last person you meet is the king.