The name McClaugherty certainly isn’t common in Ireland and seems unlikely to have been it was recorded in Ireland. The name Cloughly is fairly common (the Mc prefix was detachable and was often disregarded.). I can see a single example of Rose Ann McCloughley in Co Down which is about as close as I can get.McLaverty also springs to mind. There’s a few of them in Irish records. (Laverty being more common).McGarry is widely found in Co. Down. Many of that surname seem to be RC. Does that fit with your understanding of the family’s denomination?
This site is dedicated to Co Down and you may find some ideas and information on it:
You are looking for a marriage c 1780 and baptisms 20 years before that. Your biggest problem is that hardly any records exist from the 1700s, and so even if you knew exactly where the family came from there may not be any local records to search. Especially so if the family were RC, as very few RC parishes outside the big cities have any records for the 1700s.