What is the POD, reigning family and reason from splitting from the south ? if it is meant as a counterpart to a southern italian republic, it could used a green-white-red tricolore defaced with the royal arms assuming the southern politie use either a plain tricolore or one defaced with a different emblem (think cold war era east and west germany).
if it tries to appear neutral toward these 3 countries, it could adopt the flag use by the league of nations commission charge with administrating the area:
There is not one set of backstory to it, me and @Joshua Ben Ari always just found the idea of Second Roman Kingdom/Roman Republic to be fascinating. It can easily be a counter to the Republican South (Which the North was in favor of keeping the monarchy.) Or a buffer state between North and South.
Hmm, never thought about that before, but thanks.