I search the IFHF's online database at ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse. By 1800, they are almost non-existant. Many B/M/D events either weren't recorded, or haven't survived.
For a Peter Reilly and ? Clarke M 1840 +/- 7 yrs, Co. Cavan, with the parents' names unknown, I found just 1 record. However, the bride's forename doesn't begin with the letter "A." Your "Ann" may be a "pet" name for "Biddy," the forename on this record.
A view (usually at a small fee) of this record should show details such as parents' names, etc.