I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse. By 1800, they are nearly non-existant.
For W(illiam) Rowe B 1867 +/- 5 yrs, somewhere in Ireland, with the parents' names unknown, I found 18 record of which NONE are in Co. Wexford. Of the 18, ONE had a father forenamed Joseph. This record is in Co. Kildare.
For a William Rowe and Sar(ah) Splaine marriage in 1900 +/- 2 yrs, somewhere in Ireland, with the father's forename Joseph, I found 0 records. I'm surprised; registration was civil and mandatory after 1863. Civil records SHOULD be in this database. If not, contact the General Register Office and have them search for the certificate.