Subscription site - www.rootsireland.ie - has a record of an "Ann Mason" being baptised in Rahoon on May 14th 1812. She was Roman Catholic.
Her father was John Mason, a soldier. Rahoon is on the Western side of Galway city. Ballybane is on the Eastern side and close to the Military barracks. Marriage record for Peter McCoy and Ann Mason not found.
The name "McCoy" is not that common in County Galway. It is also recorded as "Coy" and can also be found in the adjoining county of Roscommon.
The name "Mason" is recorded in County Galway and are Church of Ireland.
Can you post the exact detail of their marriage record?