Vassal Republics? How do?

I don't really know how republics work. Do they have to be counties with a city as the primary title. How do you make that happen? Are we restricted to the ones that already exist on the campaign map?

I want to create a republic that is vassal to me. Currently I'm the King of Ireland. Is there a way that I can turn the city of Dublin into the primary title of the county and turn it into a Republic? Is that even how it would work?

Would appreciate any advice from you, my councilors.