Yes. I'm from that area, and if you have any inkling of the area you were from (Wexford is a town as well as a county, so you need to have some idea) and what the family name is, you need to contact the county records office held in the County Clinic, Grogan's Road, Wexford. Phone +353 53 9123522 .
If that fails it may be because a lot of records of that era and before are held in churches in Ireland - they held parish records of baptisms, deaths, marriages. You can contact the church in the area. If you are indeed looking for someone from the town of Wexford, contact the Parish Priest at either Rowe Street or Bride Street churches, they all live in the presbytry in School Street (+353 53-9122055).
http://www.ferns.ie/Directory%202007.pdf
If you need any more help, post back and I'll try find out more. Don't forget, if the search is outside the town of Wexford you'll need help in the particular parish, but contact Grogan's Road first. (9-5)