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 T(homas) Green B 1833 (exact), Co. Roscommon, with the parents' names unknown, I found 1 record. However the recorded forename is Thad(deus).
For a T(homas) Green and Beatrice Stanley M 1851 +/- 2 yrs, I found ZERO records.