I searched on www.rootsireland.ie for O'Brien surneam but first name blank parents James O'Brien and Mary Smith (no Ann) for all provinces and got 4 matches.
I then did the same search in Dublin only and got 1 match.
rootsireland is a pay site so I didn't get the details but if you register you can view the records for a fee.
They are having a 40% off sale til 14th July.
I hope this helps