To find the marriage without knowing the parish is going to be very difficult... or require a bit of luck.
If they married in Co. Kerry, South West Co. Cork (or the west of Cork city), or Dublin city then you might find them on
www.irishgenealogy.ie (further RC records for Dublin city are due to be added to this site later in the year) Sullivan/O'Sullivan is a common Cork/Kerry name, so it's possible that Patrick came from that area.
RC Parish records for some other parts of Ireland are available on the pay-website of the Irish Family History Foundation as
www.rootsireland.ie There are a few counties and areas not currently covered by either website.
Shane