Your best bet will be to get in touch with the genealogical centre of County Down. Civil registration of Birth, Marriage & Death Certificates, as we know them today, was not introduced in Ireland until 1864 and before then all records kept, were in the form of church or parish records. Some of these have regrettably been lost throughout the years to fire and human error,however, all surviving records from those years have been organized into these county based genealogical centres. You can find the contact details for the County Down centre, along with all other centres, on the official National Archives website:
http://www.nationalarchives.ie/genealogy1/genealogy-centres-nationwide/.