Is there a meaning for the first part of that name (Maghera)?. Where would the birth, marriage, death records of this place be stored?
The word “Maghera” means a plain or flat field. That should help explain why it appears in so many place names.
If you are looking for the statutory records of births, deaths and marriages, they are on the Familysearch site.
If you are looking for church records, then in addition to the advice already given, copies of the surviving records for the 4 Presbyterian churches in Rathfriland are held in PRONI, Belfast. They are not on-line and so you would either need to go yourself or have someone else search for you.