Taking Train from Belfast to Dublin

We're doing Belfast Central to Dublin Connolly. Translink appears to be the only rail carrier and it appears to take about 2.75 hours. As best I can tell, the schedule isn't posted until a month before hand so you can't make a reservation whenever you want. Hope this helps.

The trains leave from Belfast Central and goes to Dublin Connolly. The information is available on the national rail website. You can also buy tickets on this site. There can be discounts for booking in advance so I would checks now for the best rates on the day you are leaving.
Belfast Central is across the Largan River from the Titanic Quarter and depending on the location of your air bnb could be within walking distance. There is also a commuter train line from Belfast Central to Bangor which stops at the Titanic Quarter train stop. Depending on your exact location, this could be more convenient.

Thank you!! Paul Scales--am I safe just buying a ticket on the date I want to travel when I get to the station, or should I buy in advance?

I thought it would be cheaper if bought in advance. I saved a lot of money doing just that with Scotrail last year...

You know you can also take the bus from Belfast to Dublin. About the same amount of travel time as the train.
http://www.aircoach.ie/timetables/route-705-x-belfast-dublin-airport-dublin-city-express

The Titanic Museum is a must visit since you'll be so close. It's great. Also visit the Crumlin Road Gaol and take the Black Cab Troubles tour. Both are fascinating. Check to see whats schedule at the Lyric Theatre. Amble through St. George's Market as well as the Botanical Gardens. Visit the Ulster Museum.

Lastly, visit Mourne's Seafood next to Kelly Cellar's Pub and have the seafood chowder. Oh my.

All of those sites and more are on my list! The flat I rented is in the Titanic quarter. I'm also planning a day trip to the Giants Causeway and to see the Game of Thrones filming sites