I searched the Irish statutory marriage records for a marriage between Margaret Carson and Thomas Mortimer but did not find one. Assuming the marriage was not RC, then the records start in 1845 and so I think the couple married outside Ireland.
Carson is not a native Irish name. John Grenham's surname site suggests that Carson probably comes from Galloway (south West Scotland), and if so they’d have arrived in Ireland in the early 1600s as part of the Plantation. A huge proportion of the population of Co. Fermanagh have similar origins.
Most of the Scots settlers in Fermanagh became Church of Ireland. Looking at the 1901 census of Fermanagh there were 223 people named Carson. The vast majority were Church of Ireland or Methodists (who were originally nearly all Church of Ireland too). Trory Church of Ireland records start in 1779 (with some gaps). There’s a copy in PRONI in Belfast. They are not on-line so far as I am aware and so a personal visit is required to view them. If you can’t get there yourself you might want to employ a researcher. Researchers in the PRONI area: http://sgni.net
No Carsons in Trory in the tithe applotment records for 1825. That doesn’t mean there weren’t any living there, just none who had land.
There were none in Griffiths Valuation of Trory in 1862 suggesting they had all left by that time.
The surname Graham is also a very common surname in Co. Fermanagh. They too arrived in the 1600s from the Scottish Borders, and are renowned for being "Border Reivers" sent to Ireland by King James I because of trouble they caused on the Scottish-English borders. (If you are interested, "The Border Reivers" by Godfrey Watson, pub 1974, is good background reading. Plenty of murders and treachery.)