There should be a significant cost associated with moving the capital, enough to prevent you from doing it anytime you feel like it without thinking, but also allowing you to move it if there are very strong reasons for doing it. It should cost stability, money and possibly bring a few small DP changes with it. There should also of course be positive effects on the province moved to, and negative effects on the now ex-capital province.
The target province must have some basic requirements, like being a national province, and having a minimum tax value (I suggest it needs to have a minimum value OR just be richer than the old capital). If these are no met, the capital cannot be moved. These restrictions are realistic and will have realistic consequences. For example, it will realistically prevent France moving its capital to an over-fortified Guadaloupe just for defence purposes. Also, I assume that in EU3, like in EU2, the location of the capital does have some economic consequences which need to be considered, which in themselves dissuade too ridiculous displacements.
The best way to design a historical/realistic game is in a way that makes the player play realistically because he benefits from it.
Here are some good non-historical examples of when I'd like to move my capital, either due to practical considerations or just flavour, and it's also be historically realistic to do it:
- Order of Saint John manages to conquer Egypt from the Mameluks and moves capital to Alexandria to have a more central location.
- Scotland conquers England and moves capital south to a more central location.
- Burgundy takes French crown and moves to Paris just to show who's the new boss.
- More or less any Eastern European power conquers Istanbul and moves capital there due to the prestige of the location itself (well, the Turks actually did, but I also think almost anyone would have, especially any smaller power based in the Balkans).
To conclude - For this feature, I think the following two rules suffice:
- New capital needs to be a national province.
- New capital needs to have a certain minimum tax value OR just be richer than the old capital.
Then, the cost in temporary stability loss, possible DP changes and MONEY is the price to pay.
The rest should take care of itself by the common sense of the player. For the AI, AI events for certain locations might be the best way to guide it.