Perhaps a decision on some kind of scientific discovery, where parties are split between what to do, research it succesfully and have a chance on X, not research it and get Y, or fail to research it and get Z.

Higher % to get a succes if you're a certain government type like technocracy or some other science-focused government.

Succes rewards could be extra points: black hole research (physics points), wild life research (society points) and robotic left-overs from the past (engineering).
Failure: results in a mineral, credits or happiness debuff for a certain # of months.
Not researching: happiness buff or debuff, depending on governmental type and chance.

you could have a planetary civil war event on planets that have angry populations. option 1 Side with the planetary government: 75% chance govt will win, and if they do their pops will love you. option 2 Let them sort it out. 50/50 chance and winner will have no effect of their view on you. option 3 side with the rebels: 75% chance Rebels will win and if they do their pops will love you. option 4 (only for certain empire types) Wipe them all out: The entire planet begins to lose pops based on ships in orbit, the winning faction will become hostile towards you.

You could have a policy to fund certain rebel factions in other empires, adding to the support they gain. If they break free they become your vassal.

Prison colony: In order to put a halt to the increased violent crime, our empire is considering creating a prison colony. Option 1 Absolutely not! ethics divergence up, gain EC. Option 2 Send them to the outer reaches: get a slave colony ship that can colonize normally inhospitable worlds (all except barren, molten and gas giant) costs Minerals for colony ship. Option 3 Excecute them instead: a small % of pops on each planet will begin the purge process. all other pops gain happieness boost and ethics divergence down.

Also, If you just want some ideas, I would check out Europa Universalis IV for its events and situations, alot of them could easily be tweaked to fit a future scenario.

Hope all of this helped.

Sincerely,

your favorite government

Democracy
- You could have election events that add "support" to particular candidates making elections more unpredictable.

Oligcarchy
- Much like the above Democracy event you could have potential leadership fights and hostile takeovers that your leader has to combat.

Monarchy
- Some sort of succession crisis.
- Could have pretenders you have to neutralize before the heir takes power.

Totalitarian
- Events that boost or reduce rebelliousness.

Furthermore, just having little "flair" events and news reports reporting random but relevent things happening in your government would be pretty cool. Maybe your governors are having affairs, making good/bad decisions, having financial problems? Maybe an Admiral if having problems with fleet readiness or an incompetent one damages one of your best battleships?