Supplier Carhire say this about cross border and travel restrictions:-
Travel restrictions:-
Please note that cross border travel is permitted to the North Island. It is a requirement before traveling across the border that you inform the local car rental agent before leaving the rental location. There is an approximate 34.05 Euro (plus tax) fee applicable for border crossing into Northern Ireland.
Car rental is not allowed at any time to leave the island of Ireland. Rental vehicles must be returned to the Republic of Ireland. If the required coverage is not purchased, the renter will accept full responsibility for any recovery fees, in the event of car breakdown.