Hi Steve,
Sorry to inform you that you won't be able to get his birth certificate as the Irish Civil Registration only started in 1864.
Your best bet would be to try and determine which church his family may use to baptise him.
Another angle, the name you gave here is awfully common--how do you know the Robert O'Conner you find in the Valuations is yours??
Sorry if I am not being helpful but I am trying to raise some awareness regarding the perils of Irish records.
Kind Regards,
Tees