I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 20 M church/civil/census B/M/D records for MOST Irish counties, including Donegal. Records before 1863 are increasingly sparse - almost non-existant by 1800. Protestant records are the LEAST likely to have survived.
For Pat(rick) Bradley B 1864 (exact), Co. Donegal, with parents' forenamed Ber(nard) and Mary, I found 2 records. A view of the detailed record(s) (at a small fee) SHOULD show the parents' full names and sometimes other details.
Will leave it to you to search this database for the others.