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I assume your Michael was Roman Catholic.
I searched on the subscription site Roots Ireland and did not find a baptismal record for Michael Hennessy even though the Tullow RC records go back to 1739. However, there appears to be a gap in the baptismal records for 1802 thru May 1807 and possibly Michael was born in the gap period and his record would not be available https://registers.nli.ie/parishes/0735 I also did not find baptismal records for any children of Andrew Hennessy and a wife Bridget. Also did not see a marriage record. Perhaps the marriage and baptisms occurred in another parish which does not have records back to 1830 and earlier.