The Frenchpark records start in 1865. If your Martin was baptized in Frenchpark in 1859, a record will not be available.
If he was baptized in Fairymount then records are available back to 1833. I searched the subscription site Roots Ireland and found this record.
June 3 1856 father Patrick McGarry mother Mary Beirne witnesses Denis McGarry and Mary McGarry Fairymount