Renting a Car in Dublin and Returning In Belfast

It's not that they don't have reciprocal agreements, it is in most countries the law that car hire companies can only rent out cars that are registered in that country. This is in true virtually all countries (imagine a US car hire company trying to save money by hiring out cars registered in Mexico, or in Panama!).
So the car hire company can't hire out the car, and has to pay an employee to drive it back. And they will pass on the cost to you.

I would recommend you get a quote. As Dublin and Belfast are relatively close, the surcharge may be less than other international one-way hires.

One island, two countries. You CAN return a rental car in Belfast, but there will be a hefty one way fee involved. We don't know what your itinerary is, but perhaps picking up and dropping off in Dublin, then catching a coach bus (2 hours from Dublin Airport to Belfast city center) or the train from Dublin city center to Belfast city center would be a significantly cheaper way to go.

If your itinerary includes Donegal, one solution I've seen suggested but not personally tried is to return your Republic of Ireland registered car in Letterkenny, and take a bus / taxi to Londonderry and pick up a Northern Ireland registered there. Means two one way rentals though. Would work anywhere where there is two convenient nearby towns on opposite sides of the border.

Thanks everyone, for your comments which are all very helpful. I apologize for not replying sooner, but we are traveling, on a U.S. road trip and my laptop died. I just replaced it a few days ago and am trying to get caught-up with all computer-related things.

Jim