Formal:
* Sire: (used for a king)
* Your Highness: (used for a king, queen, prince, or princess)
* Your Royal Highness: (used for a king, queen, prince, or princess, more formal than "Your Highness")
* Your Grace: (used for a duke, duchess, or archbishop)
* Your Excellency: (used for ambassadors, governors, etc.)
* Sovereign: (used as a title for a monarch, less formal than "Your Majesty")
Informal:
* Your King/Queen: (less formal, but still respectful)
* Your Ruler: (general term for a head of state)
* Your Highness/Your Royal Highness (Can be used informally, but only when you are on familiar terms with the monarch)
The best synonym to use will depend on the specific context and the level of formality you want to convey.