hampan,
Researching in Ireland in the 1700s is very hard going due to the general lack of records. You are looking for baptisms around the 1740s and a marriage 1760s or 1770s. If the family was Presbyterian and came from the Dungannon area, then the bad news is that there are no church records that go back that far. The nearest are Dungannon 1st Presbyterian which has records from 1790 onwards. Drumcask, Cavan is in the parish of Kinawley. It doesn’t have a Presbyterian church at all. The nearest is probably Killeshandra which has baptisms from 1743 and marriages from 1741 (with gaps). There’s a copy of those records in PRONI (the public record office) in Belfast. I don’t think they are on-line anywhere so a personal visit would be required to view them.
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).