The General Register Office in Dublin has all the civil records - births, deaths and marriages -- for all 32 counties on the island up to 1922 when Northern Ireland was established.
The General Register Office of Northern Ireland was provided copies of the birth and death records before 1922 for the six counties of Northern Ireland. However, they don't have marriage records prior to 1922 and those have to be requested from the local District Registrar's Office if the marriage took place in any of the six counties of Northern Ireland. .
The General Register Office of Northern Ireland website is http://www.groni.gov.uk/index.htm
If James McGlynn was born before 1864 when civil registration started there won't be a civil birth record so you'd need to know specifically where in Tyrone he was born to contact the local church for a baptismal cert.
James marriage to Gertrude would have been in her church and they wouldn't necessarily have lived in that area.