Does anyone have a preference or advice? One way car leases can be more expensive, and I'm not sure you can drop it off in another country. On the the other hand, BritRail passes don't work in Ireland.
You could buy a Belfast to Dublin train or bus ticket.
Picking up car in one country and dropping offin another always means a drop fee, sometimes large.
For the train and bus options, see www.translink.co.uk. Tickets are only about $25.
If this Belfast to Dublin trip is the only train ride you will be taking, a train pass would be a bad value, even if it were valid for the whole trip. Just buy a single ticket.
(I'm not sure how they did it, but the various entities that sell passes have tricked people into thinking that there are no train tickets, only rail passes. There are tickets, just like you don't need an "air pass" to ride on a plane).
You can pick up a car in Belfast and return it in Dublin, but you'll pay a substantial surcharge since they are different countries.
Are you talking about car leases or rentals? They are about as much alike as apples and cinder blocks and I have never heard of a lease program that would fit your geographic constraints as the pick up and drop off points are very limited. Unless you are traveling in a large party, a train ticket (not a pass) should be cheaper.