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What was the religious denomination of your family?
I have done a number of searches on the subscription site Roots Ireland in Co. Roscommon and Co. Galway East and did not find any records for the Michael Cook/Ellen Phair family. Based on the availability of RC records for Ballintubber/Ballymoe parish https://registers.nli.ie/parishes/0541 some records should be available. If the family was Church of Ireland then we need to look for availability of records.
I also did not see a record in the 1855 Griffiths Valuation for Michael Cook in either Roscommon or East Galway.