Hi Jeanie,
Likewise I recommend the Ulster Scots Centre at Monreagh which is near Carrigans in County Donegal.
My husband (we live near the Monreagh Centre) has done a lot of work on church records - although his work relates to records held within Church of Ireland churches.
There is a strong possibility that the spelling of the surname Daugherty has been changed (unintentionally) when authorities were recording the names, ages and occupation of people who emigrated. Records were kept of all passengers travelling in the ships.
The most common spelling of the name pronounced as "Daugherty" is DOHERTY. Both of the surnames Cunningham and Doherty are commonly found in the Lagan Valley.
I hope you are successful in tracing your ancestors. Some of the graveyards now have plaques listing the names of people buried there. This can also be a useful way of tracing families, but I don't know who holds lists of names from the graveyards. Most graveyards until relatively recently were owned and maintained by the individual churches. Many graveyards now are managed by the local council for the area.
I hope this information may be of some help.
Best wishes,
Anne
Anne Speers.
http://www.finnvalleycottages.com