The
RPSI have a small stock of preserved trains and carriages up at Whitehead, north of Belfast on the Larne line, and they run a number of charters throughout the year in NI and the RoI.
NIR services have improved dramatically over the last five years. The CAF-built C3K stock are now in full service and the first of the follow-on C4K units is apparently scheduled to arrive in Belfast today. When the 20 units are here, there should be an entirely modernised fleet, so depending on your penchant for thumpers, you might want to head over sooner rather than later. The obscure 'Castle' class 450 trains, which predominantly serve the Larne Line and the ancient class 80s (now reformed as four-car units with two driving units for reliability) are not long for this world.
Meanwhile the Enterprise to Dublin is just divine. Slow, frequently delayed, but a taste of how intercity trains ought to be. Don't bother with first class, standard class has big squishy seats and a very comfortable atmosphere. £10 daytrips to Dublin always available online from Translink.