I am trying to trace the family of John HORGAN b approx 1831. in Co. Cork Ireland !

His death certificate gives the following information.
Father. Jeremiah HORGAN
Mother Ellen HORGAN ( ms unknown)
He married Elizabeth DYER in Coolbanagher, Laois 20/Aug 1861 and they travelled to New Zealand onboard the "MYSTERY" ( great name!) Oct 1861
If anyone could give me any idea on how to find a birth in Cork I would be very grateful.
Elizabeth was COI and as they didn't marry in a church, I don't really know if he was too, although he is buried in the Anglican side of the cemetery in Waimate NZ.
many thanks, Mila