The Police Service of Northern Ireland maintains an online register of missing persons cases from the province. There are 20 people listed, some dating back as far as 1962. You can browse the list or filter the results by region and time frame. Note that the register does not appear to be updated with recent cases, and you may be better served elsewhere if this is what you are seeking.
There is also information, including numbers and an online form, for placing a missing persons report. There is also resources and detailed information on what to do when someone goes missing.