Hi, What Port did they land?
Trove have the Ports to search by, then the year.
I don't have access to Trove now, sorry.
You won't find hardly any early Births and Marriages. Deaths avery few. Church records are very few.
Civil records are from 1864.
BUT, there are places to search.
I searched Gre* and found a William Grehan in Doonfeeny, in the Diocese of Kilalla, in 1834. This is in the area of Ballycastle.
Others close by, see this link..............
The Tithe Applotment Books, 1823-37 (nationalarchives.ie)
Catholic Parish Registers at the NLI
Let me know the Port and I will see if I can find the family.