Your main options are via EWR (CO), or LHR (BD/EI). There are other low-cost options from the UK mainland, but you'll need to re-check (with no guaranteed connections), and may be subject to harsh baggage restrictions and/or fees.

As an alternative, if you have an easy direct flight to Dublin, there is a bus from Dublin airport direct to Belfast, taking 2h25. Note that, though, transiting via Ireland, it does get a little complex as far as immigration is concerned.