Hi,
Patrick per 1891 was born 1864/5 in Cork North. His birth should have been registered in Ireland. For the early years there was an amount of non-compliance but on the plus side, the registered birth 1864-6 or so are in the IGI database.
There are 5 Patrick Healy from Co Cork, with father PAtrick also
03 JUL 1866 0494, Mallow District, Cork, Ireland
17 MAR 1866 0246, Ballineen, Cork, Ireland
06 MAR 1867 0904, Mitchelstown District, Cork, Ireland
13 APR 1865 0145, Cork, Cork, Ireland
24 NOV 1866 0140, Cork, Cork, Ireland
I would dismiss the last 2 as not 'North' and Ballineen is West in my book.
The only Daniel is 27 JUN 1868 0259, Kanturk, Cork, Ireland
but he could have been born before general registration began. Do you know when he was born?
Kate