Miller and Nobles

You don't say what denomination the couple were. That's normally required to trace any relevant church records. However in this case no church in Coleraine has any reocrds for the late 1700s, so there are probably no surviving records of either the baptisms or marriage you are seeking. If you are looking for living descendnats, DNA testing may be the only way forward.

This is one of the most elusive couples I've ever researched.  I don't know what religion they were in Ireland or in the US.  There aren't any records in either country except a land purchase and sale of the same land in Illinois in 1840.  The only real evidence they lived are the records of their children who knew the names of their parents.  One old family record states they came from Coleraine New York, but there never was such a place.  A couple who were close friends and moved with them at least twice has a family tradition that they came from Ireland.  There are living descendants in the US, but we need some in Ireland to do any matching.  Would that be You?

No I am not related to either family. I am a volunteer with Ireland Reaching Our who lives near Coleraine.

Both Noble and Miller/Millar are common names in Ulster. Most are Presbyterian or Church of Ireland (Episcopalian) and descended from Scots who came to Ireland in the 1600s either as a part of the Plantation of Ireland or as famine refugees in the 1690s when Scotland was badly affected by famine. That they later left for the US in the 1700s also tends to fit that profile. (Native Irish migration really only started in big numbers in the 1800s. Most emigrants from Ireland, and Ulster in particular, in the 1700s were Presbyterian or Church of Ireland).

Looking at the 1901 Irish census there were 6250 people named Miller, of whom 873 lived in Co Derry/Londonderry. 1112 Nobles, 22 in Derry/Londonderry.

I’d suggest you put your DNA on some of the sharing DNA sites and see if you get any matches on this side of the pond. Given the likely family background I have mentioned, you might find matches in Scotland as well as Ireland.