You will be interested to note that the Wexford birth records will be on line soon. I've been saying that for a year but they are now pending. These will be available on a History Foundation not for profit but fee paying website although the fee is small there were a lot of Roach/Roche in Wexford so you would need to be careful.

Have you tried the Tithe Records for the 1820's or the
Griffith Valuations of 1853. These are both used as census substitutes as there are no complete census until 1901.
The Tithe are available on Ancestry.com since last fall and the Griffiths www.askaboutireland.ie I would use the website
www.failteromhat.com first as it is simpler and look for
common Parish's for both Roach and Mooney.(*see below)

The Parish being the single most important thing to know.
Even if you get it down to 2-3 parishes its a better start than 143.

In 1853 there were 12 Mooney's in Wexford and 436 Roche's.
If your William was still in Wexford
in 1853 he would of been about 57-60 and an occupier of land.

There were 12 Mooney's and 21 William Roche/Roache's, but the surnames names have only one parish in common (which is no guarantee) and that is the Parish of St. Mary, Newtownbarry, Enniscorthy.

William Roche Parish St.Mary, Newtownbarry, Townland Ballyphilip tenant of H.B. Bridges #13 house, outbuilding and land 37 acres 0 roods and 19 perches.(IF this is the right one) I would need to know how bar NTB records go back to know if a person born in 1796 would still exist, they probably married around 1818 and might have survived. If they weren't destroyed in 1798 or the fire of 1922 if they were taken care of they might exist.

RC records kept in local custody but some old Wexford records might be available on microfilm on the Latter Day Saints website. These are the records from the National Library in Dublin's records which require in person research.Protestant records prior to 1899 are kept at the Church of Ireland's representative library in Dublin.

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