So this is the baptism you believe is Michael
https://registers.nli.ie/registers/vtls000632917#page/46/mode/1up
Right hand page born 1st Nov baptised 16th
I'm not seeing a civil cert for him.
That's the one I found. Other documentation is all over the place: US censuses put his DOB in 1867, 1867, and 1872; marriage in MA puts YOB as 1867, and one census had his DOB in June (the US census was done in June, so they might have mixed it up), but his naturalization doc has Nov. 1, 1872 - while the day and month align, the year doesn't, but if he claimed to be younger when he arrived, he could waive the court fee, so I don't worry about the year as much and he may have claimed 1872 in the census to be consistent after citizenship. I think there's enough with the dates, names and location to conclude that's him.
I found a 1901 census with Patrick Mannion and Mary, with children Anne and Elizabeth. I have documentation that his other three sisters moved to the US, but not those two; however, their ages indicate birth years of 1878 and 1882, so that's off by a bit - but as indicated below, his parents should have been alive in 1901 (the census lists them as 80 and 60).
Michael purchased a life insurance policy in September 1902 that indicated he was 28 on his last birthday (indicating a YOB of 1873 if he was born in November, but again, he may have had an incentive to present himself younger than he was). He claimed both of his parents were still alive (father Patrick Mannion 75, mother Mary Harney, 63 - not far off from the census above). The application indicated that he had two brothers, both of whom died in infancy, and five sisters, all of whom were alive, despite a contradictory notation indicating that two sisters died in 1877 of typhus. I haven't been able to find anything to confirm those deaths.
Michael's wife was Mary Barrett (Mary's parents were Thomas Barrett and Bridget Rush); I found a birth record from Dec. 13, 1866 for Mary Barret born to Thomas Barrett and Bridget Rush in Galway; I also found a birth on Oct 17, 1874 for a possible sister named Catherine in Tuam, Maylough and another birth for a child named Bridget to the same parents. I found a passenger list from 1884 for a ship from Galway to Boston that included a Bridget Barrett, 35, Mary, 16 (indicating a YOB of 1868), Kate, 14 (possibly Catherine, but she should have been 10), as well as another Bridget, 12 and several other children - with no husband/father. This could be my Mary, but there's not much else to go on, other than it suggests that Mary's father Thomas must have died by 1884.
I also found a record for Thomas Barrett, born Nov. 3, 1833 in Rahoon, Galway to Thomas Barrett and Mary Keary, as well as a Bridget Rush, born Dec. 27, 1834, also in Rahoon to Thomas Rush and Mary Flaherty - no way to know if they're connected.