Essentially what the question says: I'm looking to rent a car in Northern Cyprus, and occasionally take it across the border to the Republic.
I know few companies will issue the necessary cross-border permit.
Which ones do?
The North Cypriot companies I've found allowing cross-border travel are Esentepe Brisk (what I ended up going for) Oscars and Baspinar.
You buy an EU Cypriot insurance at the border for €25 lasting a month.