The diplomacy of this game is great. These are just a few ideas I'd personally like to see. Some of these are straight forward diplomacy, while others are more or less good will missions and gameplay tweaks.
1) Option to request a non-enemy faction stop attacking a player's ally. This could also be a threat, implying the player's wrath if not complied with.
2) Food trading. I always imagined this would be one of the top resources a faction might request.
3) Medical aid. When the virus event happens it would be nice if you could ask a friendly faction to treat your planet. Also additional contagions might make things more interesting if this mechanic were implemented.
4) Returning planets captured by invasion. I would like to see more interest or persistence by the AI to recapture their fallen planets. Also I'd like more relationship points or trade value for returning an AI faction's planet to them after I capture it. Sometimes my allies just become complacent forcing me to do all the fighting for them. I'll give them stations, ships, troops and they make horrible strategic decisions.
5) Military Alliances. It would be nice if the effects from Military stations transferred to allies when in the area of effect. Also I'd like alliance to allow ship parking in allied stations and on planets. This makes it easier to help them with defense.