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Welcome to Ireland Reaching Out!
I assume your Mary Green was RC? The online parish register for Kilcock https://registers.nli.ie/parishes/0708 goes up to 1883, The register shows a record gap from 1791 to August 1816. So if Mary was born prior to August 1816, a record will not be available.
The Church of Ireland records for Kilcock are not available around 1816.
Let me know if you have questions.
Castlemore Roscommon, IrelandXO Volunteer ☘