Is the marriage cert you have for Robert a Civil or Church? I would suggest you get whichever one you DON'T already have as there's a possibility that will give the father's name (I had the same situation a few years ago).
Who are the witnesses - any relation?
Who is Robert's mother?
Do you know if Robert had siblings?
Did Robert have sons? If so, did he name any of them Barney/Bernard?
Do you have his children's birth or baptism certs - perhaps one of the witnesses was a Sheridan?
Who was Robert's wife?
The more info you can give, the more help the list can give you.
Happy Xmas to you too!