I can't give precise info, but will try to give you tools to find it.
I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
Note 4 - Each parish's rcds have their own quirks and limitations, too many to enumerate individually.
For Michael Connors M 1902 +/- 4 yrs in Co. Roscommon, I found 5 M rcds: 1898, 2-1899, 1903, and 1904.
For Bridget Kane M ditto, I found 6 M rcds: 2-1898, 2-1899, 1901, and 1903.
With the above, search this database and find the Roscommon parishes where these M events occurred. If you find matching parishes, this is highly likely to be for your ancestor.
For Mary Connor B 1906 +/- 4 yrs in Roscommon with a father forenamed Michael, I found 0 B rcds.
Google the foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genform msg.