Maybe make an estate called 'Bucaneers' or something to represent privateers overseas. It'd be available for countries that have any overseas territory or sth. While having positive influence/loyalty they would give very strong bonuses to privateering and trade steering. One of the actions could be to ask them for a captain? And then if they would get too little loyalty several pirate fleets would spawn in an overseas trade node where the target country has enough trade power and also that would trigger (a chance for) a pirate republic spawn in one/two provinces in the said trade node. As long as this country is alive, more and more pirate fleets would spawn.
When I think of it, I will turn this into a mod one day, so reserved etc.
Also please, please, if you consider this, give pirates a better chance for capturing enemy ships in a battle.