Daniel, would you enter Henry's profile ID on your question? That may give us more information to work with! Thanks!
What marriage source are you using for his marriage? Unless it was one of those rare cross Denominational marriages with a Catholic woman, if he was married in the Church of Ireland he would be baptised Church of Ireland.
From his time in Canada, what did he say about his religion and place of birth on the censuses? Where was he buried, in a Catholic or Protestant graveyard? Take a look for a death notice in any contemporary newspapers. Does he appear on Find A Grave - many ex-pat Irish have headstones reflecting their religion and also sometimes where they came from.
As Wayne said in his reply, a lot of Church of Ireland church registers were destroyed, but it was when there was a fire at the archives of the Four Courts in Dublin during the Irish Civil War in 1922. All the pre-1901 census records and Wills proved in Dublin were destroyed in the fire as well.
Any surviving Church of Ireland registers for Eire (Southern Ireland) are held in the Representative Church Body library in Dublin. They are not on line ... yet. There is a plan to get them indexed and on-line in the next couple of years.
The surviving registers for the parishes for the six counties that now make up Northern Ireland are at PRONI, the Public Records Office of Northern Ireland. Again, not on line.