So far I like the scheme I've seen in Canada best, provincial parks are tagged as:
boundary=national_park
boundary:type=protected_area

I would also add:
protection_title=State Park
and
ownership=state rather than admin_level=4, but both seems about equally used right now.

That way you get a rendering with the national_park green dotted line for now, and if/when protected_area starts getting rendered someone can easily use a bot to change the boundary.