Without further details on the address I am not certain of which parish would apply for Abbey street as it is divided into three section and extends on both the east and west sides of Sackville (now O'Connell) street. These are the details based on what I can locate for slightly later times between about 1840 to 1870.
Lower Abbey Street runs from the east of Sackville st towards the Custom house and is in the Civil Parish of St. Thomas. At the time St Thomas Church was located at the northern end of Marlborugh St., but was destroyed in 1922 and rebuilt just off the original street on Cathal Brugha Street.
Middle Abbey Street runs to the west of Sackville st as far as Jervis Street, and is partially in the parish of St. Thomas and partially in the parish of St. Mary. The building still exists but is now a restaurant.
The remaining section (Upper Abbey Street) runs on further to the west as far as Capel street, and is also in St. Mary's Parish.
I presume an Archbishop of Dublin at the time would be based at one of the Cathedrals
the
Cathedral - Christ Churchor
St. Patrick's CathedralThe first appears to be in the parish of St. John and the second in St. Nicolas Without.
Marlborough street is just to the north of Abbey Street and to the north of the river Liffey. Christ Church is on the south of Dublin city and near to Dublin Castle etc..and St. Patrick's is a little further south on Patrick Street.
Shane