Pam,
There aren’t many Glovers in the 1901 census of Fermanagh but the 2 families that are listed were Church of Ireland (ie Anglican). Coulter is a lot more common with over 200. Most are again Church of Ireland with a few Methodists (who would have been COI earlier in the 1800s), a few Catholics, a handful of Presbyterians and the odd Brethren. But, by far, Church of Ireland is the most common denomination.
Whatever the denomination, a marriage c 1869 -1872 should be in the Irish statutory records. But I can’t find it.
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).
The 4 surnames you have listed are all settler surnames, so it’s likely that the families all originated in Scotland and/or England and moved to Fermanagh in the 1600s as part of the Plantation.