A few Irish records that may help.
Dublin St Lukes. Baptism 28 Feb 1758 Archibald Stephenson son of Robert and Izabela Stephenson.
Dublin Rathmines. Marriage 20 April 1870 Thomas Stevenson of 66 Portland St Glasgow, journalist, father Archibald Stevenson. to Maria Tieran of 27 Cullenswood Av. [Dublin?] father Michael Tieran.
There is also a burial for an Archibald Stephenson of Patrick St. Dublin St Nicholas without. 2 Dec 1718