The different factions have the following tools to interact:
Declaring war for a specific neighboring sector
Giving gifts / send diplomatic ship to improve relations
Insult to lower relations
Trade agreements (allowing ships to buy/sell from other factions assets)
Passage agreements (using jumpgates from other factions to get to their sectors)
Military/Alliance agreements (both factions using military ships as one)
Give/sell/ask for a sector to improve relation or get money or remove a threat
Each faction has values that can be used: diplomatic power (how persuasive is a faction), xenophobia (how resistant is a faction to offers from another (to balance diplomatic power), how warlike or "tradelike" is the faction and so on. Most of it heavily influenced by 4X games.
Going to war is easy, but for the rest, like making alliances, allowing ship passage / trading and so on in a believable way, I am kinda lost. I don't really see a sort of generic algorithm that would make AI controlled factions using diplomacy without relying on a nightmarish mess of nested If/else/if/else. While I am fairly used to FSM logics which i used (to an extend) for individual units I don't really see that working on a faction level.
The major problem I see in this description of diplomacy is that most of it consists of arbitrary abstractions and ritual behaviour and it doesn't lend itself to translation into rules and game theory (which you need to have an AI that reasons in meaningful ways).
If factions are interested in their own prosperity (as opposed to hurting themselves to hurt others more, e.g. going to war) they can simply be friendly with everybody: reciprocal trade and passage agreements, occasional fair exchanges of territories for good reasons, massive military alliances (marking the few rogue factions outside the alliance as a potential threat), no wars, no gifts, no insults, no bad relationships, no persuasion, no xenophobia. Strategy would consist of being ready to go to war with neighbours that aren't in the alliance in case they do something funny.
This style of AI would have to evaluate the economical benefit from trade and passage agreements (maybe a Monte Carlo simulation of commerce and travel with and without the agreement) and the best selection and deployment of military forces (maybe more suitable for thorough searching over move trees containing fleet movements, battles etc.).