Rebelion mechanics improvement

I agree that rebellion (and anarchy) needs work, but two issues with your premise:

• It doesn't spawn 2 ships. The amount varies.
• You ignored anarchy, which comes to easily and may cause rebellions.

Systems conquered in war appear to be mutinous for several turns, regardless of approval (even at 100%). Yet I couldn't find any info on how long. Some clarity is needed. 

The above causes anarchy because an empire turns anarchic even if only a minority of systems is mutinous. This is not okay. It's especially perplexing when you have Saints & Sinners active or an empire approval of more than 95%. (Once the anarchy starts, you lose Saints & Sinners and will have long lasting approval issues or, in the latter case, most of your systems stay at 100% approval and you recover quickly. Why was there anarchy in the first place?). Make individual rebellions stronger, but empire-wide anarchy should only occur when there is an empire-wide approval issue.

I like the idea of rebellions being invasions only. Also, one system rebelling should not be easily dealt with, even if the system has good defenses. The system should be crippled* until it's over too. This would make empire-wide rebellions impossible to deal with, though. (As opposed to currently: like a mosquito attacking an elephant.)

Now I'm going to suggest a big change.

Nearby mutinous systems should unite and rebel together. First, they need a name (randomy generated based on system names and demands, e.g. "Procyon Independence Faction", "Procyon Freedom Army"). This happens even if it's just a single systems. This "rebel faction" will not rebel instantly, instead their population decides how often (every X turns) they spawn rebel forces (which initiate an invasion) on one of their systems. Furthermore, all empires can interact with them diplomatically.

Should they succeed in conquering any amount of systems they either join another existing empire or create a new one (AI controlled). Which of those two they intend to do should be reflected in their name and demands, which they'll issue when the faction is created.

Diplomatic actions are very different to the usual ones and you can also support to rebel factions of other empires. Should a new empire be created, their diplomatic relationship to other empires depends on how they were treated by them. The default is friendly. They will be hostile to their former overlord, unless they seceded peacefully. They will be more friendly towards empires that supported them by recognising their claim to sovereignty, etc.

Example diplomacy for rebel factions within your empire:

• "Grand Demands": All systems are immediately granted independence or join another empire.
• "Appease": Costs influence and a random luxury resource they demand. Rebel forces spawn less often.
• "Suppress": Costs influence and manpower. Rebel forces spawn less often.

Example diplomacy for rebel factions without your empire:

• "Enter Diplomatic Relations": Recognises their sovereignty and rebel forces spawn more often.
• "Send Military Support": Sends a civilian ship that supplies them with production*.
• "Send Covert Support": Same as previous, but requires Deniable Operations. When such ships are intercepted, you won't be able to tell who they came from.

*They could hijack the production queue. I.e. your production queue stops progressing while rebel forces are invading and they start producing military ships.

This kind of rebel system can also be used for internal politics. Rebel forces could demand government form changes, etc. instead of secession.