The problem with modeling the commune is not just that CK2 republics don't fit, but that its independence was rather dubious - the Senate was at peace with the Pope as often as it was at odds with him, and their relationship depended on who occupied the throne and how they ruled. Eugene III negotiated his way back into Rome only to get kicked out again, repeatedly; Anastasius IV, because he was a peaceable geriatric Roman, had little trouble from the Senate; Hadrian IV came to blows with them almost immediately and needed an interdict and imperial aid to recover the city. The Commune only occasionally and briefly acted like an independent state; much of the time the Senate was just trying to get a better deal from the pope (and sometimes just wanted him to give them money), or occasionally trying to place itself under special imperial protection as an alternative to direct papal rule.
The most accurate and game-compatible solution is probably to force a regency on the Pope similar to the Caliph's "court anarchy," representing that the Pope still reigns in principle but has been forced out of his own capital and is unable to properly rule. (I don't know if you can force a particular regent, but if you could that would also be helpful to put someone like Pierleoni in charge) This could be removed after a period of time, by a particularly skilled pope, or some sequence of events - or you could even give an event to the Emperor allowing him to march in and quash the rebellion as part of his coronation process (as Barbarossa did), restoring the Pope to his throne, although Hadrian IV still had some trouble with the Senate even after the imperial expedition and the death of Arnold.
Unfortunately that's not very fun in the sense of making a playable Roman state, but your options there are limited until Paradox sees fit to create playable "inland republics" that aren't based on maritime trade.
The most accurate and game-compatible solution is probably to force a regency on the Pope similar to the Caliph's "court anarchy," representing that the Pope still reigns in principle but has been forced out of his own capital and is unable to properly rule. (I don't know if you can force a particular regent, but if you could that would also be helpful to put someone like Pierleoni in charge) This could be removed after a period of time, by a particularly skilled pope, or some sequence of events - or you could even give an event to the Emperor allowing him to march in and quash the rebellion as part of his coronation process (as Barbarossa did), restoring the Pope to his throne, although Hadrian IV still had some trouble with the Senate even after the imperial expedition and the death of Arnold.
Unfortunately that's not very fun in the sense of making a playable Roman state, but your options there are limited until Paradox sees fit to create playable "inland republics" that aren't based on maritime trade.
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