Well it might be helpful to say exactly what the Pope’s powers are, and how they affected things historically. Using that as a basis, it could then be brainstormed how to represent these things in a game. A non-exhaustive list would include:
1) Excommunication: An act whereby someone is banned from participating in the sacraments, except for the sacrament of reconciliation, or participating in the liturgy in a ministerial capacity. In some cases, though not always, absolves subjects from obeying ruler excommunicated (such as in
Regnans in Excelsis).
2) Interdict: An act whereby the church suspends all public worship and withdraws the church’s sacraments in an entire area, such as a city or country.
3) Appoint of church officials: A source of money if the offices are sold, also a source of political power in some parts of Europe as certain church offices overlapped with secular offices and powers.
4) Papal Bulls: Formal public communication. Countries listened to the bull as they wished, for example, the bull Inter caetera was virtually ignored by France and England.
5) Give annulments and divorces: A fairly powerful tool in some instances, as if a wife was barren, only an official annulment/divorce would allow for a sovereign to remarry and thus produce an heir.
6) Rights as secular ruler over Papal States
7) Prerogative to crown Holy Roman Emperor
8) Sole authority to announce a crusade
9) Right to establish and dissolve religious order, and in some cases had sole oversight over religious order
10) Oversees church finances
So in a NES when the Pope says A and King of France opposes, what choices should the Pope have to enforce his will? Basically, I see two ways: promise of gain or threat of punishment. The promise of gain would include 3, 4 (in some instance such as Inter caetera), 5, 10, and perhaps in certain cases 8 and 9. The threat of punishment would be 1, 2, 6 (military force), and in some cases 4.
Under promise of gain, 5 should be ignored, for as much as I would like seeing it, it is unlikely that NESes will have that kind of detail where marriage and annulments would have a big effect. 4, 8, 9, and 10 are in minimal ways already built into most NESes. That leaves 3 as the most logical expansion for Papal powers in NESes, though again, it might be too much detail for most NESes to handle.
Under threats 6 is already in most NESes, which leaves 1, 2, and 4. Historically 4 has been the weakest threat, see, for example the papal bull Scimus Fili, which condemned the 1296 English invasion of Scotland, and which had no impact in England (though perhaps one could argue in strengthened resistance in Scotland and made France more willing to intervene). Thus the question becomes, if 1 or 2 are actually carried out, what its affects should be. Effects that fall outside the moderator’s purview would include an increased likelihood of foreign intervention (such as the Spanish Armada as a result of Regnans in Excelsis, though on the opposite side, see the French King Philippe II’s unwillingness to act against the previously excommunicated Catharism nobles until a crusade was called). Effects that fall inside the moderator’s purview would include an increased likelihood of dissident groups to increase their dissidence. For example, when the Holy Roman Emperor Gregory VII was excommunicated the German aristocracy launched a rebellion (though the fact that they were already dissident is shown by their second rebellion, the Great Saxon Revolt, which started after the excommunication of Gregory VII had been lifted). On the opposite side, Elizabeth of England, when she was excommunicated, acted so harshly to squash potential traitors, that those dissident groups that would theoretically increase their dissidence were already dead, in prison, or exiled. In my opinion, then, it is not that there is a rule “upon excommunication dissidence will rise x%” but rather “upon excommunication pre-existing rivals and dissident groups will take advantage of the excommunication in order to increase in strength, and perhaps act.”