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 a Mary Lester B 1841 +/- 5 yrs, Co. Roscommon, with the parent's names unknown, I found 4 records. However NONE have a father's forename of T(homas), or mother H(anora).