To unlock Duke and King enter Tournament mode and choose singles matches. Beat the tournament without the computer winning a game. ( not point ) Depending on your Ranking you will be challenged by either Duke or King. Total of D or worse gets you King, total of C or better gets your Duke. Beat the challenger to unlock that player. For an easier time change settings to "very easy" and 1 game sets. Duke and King are hard so get good with cross court and slam shots.

Unlockable - How to Unlock

Duke - Beat in tournament mode after flawless C ranking or better.
King - Beat in tournament mode after flawless D ranking or worse.