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I searched on the subscription site Roots Ireland and there were no Michael Madden baptismal records in Co. Galway around 1804 with father John. There were also no Madden/Conahy marriage records. Very few (two) RC parishes in Co. Galway have records back to 1804.
You could add Michael Madden to our XO Chronicles site and possibly someone will see a connection. https://irelandxo.com/ireland-xo/history-and-genealogy/ancestor-database