The Horde, Swiss and Burgundian will always emerge at set time, the Papist however will only re-emerge if they existed in Rome before, if if you take out they faction altogether then they can't come back. Here is the deal, "if they existed in Rome before" what you can do is mod out ID_ROME from the game (or make a blank region and make that Rome like sahara - with no neighbour so the Papist will never get hold of it from the rebels,) the Papist will get one life only. Don't try the same with the other emerging factions, the only thing you can do with them for the time being is the fiddle with the year to stop them hitting their birthday. 1230 for the horde, 1280 - 1453 for Swiss. 1350 - 1453 for the Burgundian. I suppose you could give them their only little islands so they don't play a part on you campaign, but you'll still get their messages.
Copied over from FAQ Question to Eat Cold Steel about modding the Pope out of the Game...LOS