I'd like to see some sort of diplomatic negotiation minigame of sorts where you basically build a treaty or agreement between two conflicting parties.
You would start by talking to each side, figuring out what they want through dialogue. Then you would start the minigame, where you have 3 windows and a status bar determining the favorable status of each side. Windows on the left and right contain stipulations that you can drag into the center window representing the agreement. Stipulations will affect the favorable status bar for each side depending on what they desire from the treaty. The goal is to build an agreement that results in or comes close to 50/50 favorable status for both sides. Afterward, you must face a dreaded random number generator (that we all hate I'm sure) that determines whether or not the negotiations were successful. You have a higher chance of success the closer you are towards a 50/50 compromise. Reaching 50/50 is a 100% chance of success.
Rewards could be based on how close you came to 50/50. Dilithium ore, diplomatic xp, expertise. Other rewards would vary based on what kind of treaty you made; Trade xp for a trade agreement, military xp for a peace treaty, colonial xp for a colonizing a planet, etc.