The problem is 'Wexford' - is that somewhere in County Wexford or the town ?
You need to know the name of the parish he was baptized in to search registers. That's why I suggested the online option...even though that's not fully available yet
Which Dublin parish was Patrick married in ? I didn't see the marriage on IrishGenealogy
There's doesn't seem to be any Robert Deegan on Griffith's valuation, but there are other Deegans. One near Enniscorthy, most of the other listings seem to relate to a Jane Deegan in the civil parish of Ambrosetown.
see :
Deegan entries, GriffithsShane
re Heywood's post - often current residence for Parents in RC marriages in Dublin city, and usually just the name of the nearest large town if the location was outside Dublin.