John Coleman 1848 : Short Biography

I live near Toronto in Canada and am descended from a Great Grandfather (John Coleman, sometimes spelled JNO) who came here from Ireland (by way of England) in 1879. He was born between 1845 and 1850.
We believe he was from Ballaghaderreen, County Roscommon but before 1898 it was in County Mayo. He was a policeman in Ireland 1866 to 1872 and we think he was the only child of Michael Coleman, a farmer.
We don’t know his mother’s name or if he had siblings. We assume, since we know of no siblings and she isn’t in census records, that she died in childbirth for John. It was during the famine years so it’s likely correct.
John was a police officer in Ireland (RIC), near Galway then later in Liverpool and then Yorkshire (1877-79) before marrying Anne Eliza Shaw from Yorkshire (Muston) and emigrating to Simcoe ON in Canada in Jan 1879. His firstborn was my grandfather William Francis Coleman in Nov 1879. My father was William Michael Coleman and his brother was John Redmond Coleman (both born in Montreal 1911 and 1918). So, we think perhaps the name William and middle names Francis and Redmond may be honouring ancestors of John and Michael, perhaps one is the maiden name of his mother. My father used both names for my brothers.
We do know that John went to Ireland one last time, presumably to tend to his dying father for the last 3 months in 1903. (Oct to Dec). John resigned from the Montreal police force in order to make the trip.
Michael likely died in December 1903 before John’s return. In one of his RIC police records John stated he had previously worked for a James Coleman – as a Labourer (probably farming) and James was very possibly another relative. We don’t know anything about parish names or townlands. He did seem to spell the town name as “Ballaghaderine” and we thought this was a mis-spell or from Gaelic but perhaps it’s a subsection of the city Ballaghadereen ???
Here's a really confusing fact – John’s headstone in Montreal reads “A Native of County Clare Ireland”. His RIC police paperwork indicates Ballaghadereen (erine) as his birthplace in Ireland.
We think his widow made an error on the tombstone but there is no way to know. A search of County Clare records did not yield any success. Maybe on his deathbed Michael told John he was actually born in County Clare? Our best hope is that a DNA connection to a resident of Ballaghadereen would provide conclusive info on Michael, his wife and their respective ancestors. I’m still hoping this happens since public records haven’t helped.
Would appreciate any info you can provide from church records. It’s my understanding that before 1864 the birth records were kept only by the church, not the civic authority. Hopefully you can find a John and Michael Coleman in the right time period and can fill in any blanks for me.
If you are a member of the Ancestry website or have any relatives that are members please let me know their names. I can try to find them in the and work backwards to see if we have common family tree links or distant DNA connections.