Hi Liane, you are out of luck, baptisms for the parish only commence in November 1811, oddly marriages commence in 1797 and on the off chance the parents were married around that time and there is one marriage but in 1801, it is a James Galvin and a Anna Rigney. That is the only record that is reasonably available for the area, there are two Galvins born in Daingean but that is not close and there is not Patick, the births are in 1797 and 1798 to two different parents. https://registers.nli.ie/parishes/0149
The only information I can offer is the name is from a Gaelic sept (clan) from Clare and the Gaelic meaning is Bright (Geall) and White (Bhain) this from McLysaghts Surnames of Ireland.
If by some fluke the marriage is correct, the name Rigney is unusual in Ireland.
I had a look in the Tithe Applottments, a tax record for landholders from 1824 to 1838, referring back to the marriage I see there is a Galvin Rigny listed, unfortunatly not in the Banagehr area but sourth of Tullamore, I wonder if Banagher was the enlistment place, the military barracks was in Birr but may have been later.
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
This is just information Liane and not a proper research but if interested you could see what the local history section of the library in Offaly has on the Galvin Rigny name. The records are all Catholic but the search would have brought back all available.
Good Luck
Pat