Hi, I really have very little experience with Ireland, and you may already have this info.
But in the 1911 Census records, a Patrick McGivern (head) is in Belfast.
Patrick McGivern abt 1853 County Down Newry Street, Warrenpoint, Down, Ireland Head
The same census narrowed to Belfast gives a number of hits that may be useful to you.
I also understand that there was a Public Records Office fire in 1922 that destroyed a lot of records.
Good luck