Well, assuming you mean a Nationalist majority (as currently the Catholic community is pretty evenly split between Nationalists and Unionists, with either side having the majority depending on what poll you look at).
Honestly, the Republic and Westminster work out some way to molify them without the province actually joining the Republic, perhaps through some new ministerial post. The Peace process is delicate enough as it is in the mid 2000s (remember it's barely 15 years since Good Friday today, and the Assembly was prorogued for a bit in 2002). The Republic, even at the height of the economic boom, just dosen't have the finances, resources or political inclinations to take over the job of providing security services in the north, and deal with the much larger (percentage wise) civil service, and that's without a more militant unionist presence.