I search the IFHF's online database at ROOTSIRELAND.IE. It has abt 20 M church/civil/census/etc B/M/D records for MOST Irish counties. Records before 1863 become sparse - almost non-existant before 1800. Protestant records were the least likely to survive.
For Pat(rick) Bradley B 1864 (exact), Co. Donegal, with the parents' names unknown, I found 2 records. Father's forename for both is Bernard, mother's both Mary. This suggests they may be duplicate records of the same event: likely one church and one civil record.
For Mary O'Donnell B 1873 (exact), ditto, I found 18 records. However, only ONE has a recorded middle name of Ann. Father's forename for this record is James, mother's Susan.
The above seem HIGHLY likely for your ancestors. A view of the detailed records SHOULD reveal info as to parish, maiden names, and sometimes other items. If you decide they are for your ancestors, you have a chance of finding their parents' marriage records, likely also in Donegal.