I have never heard of any church in Ballymena named Fairview. Perhaps it’s an old name that is now obsolete. However if it is, I can’t find any reference to it. There are the following Presbyterian Churches in the town:
1. Non subscribing Pres
2. Ballymena 1st Presbyterian
3. Ballymena 2nd Presbyterian, also known as High Kirk
4. Wellington St Presbyterian
5. West Church Presbyterian
6. Reformed Presbyterian (Covenanter)
Not all of those churches were in existence in the 1700s. None has any records for the 1700s though.
Presbyterians in Ireland don’t use the parish system. The church you attend is a matter of choice and may not be the nearest to where you live.
Broughshane is about 2 miles east of Ballymena. In the 1700s there was 1 Presbyterian church there. There was also one in Buckna just outside Broughshane, though I don’t know when it was established. There was one in Clough a couple of miles north of Broughshane. It opened in the 1670s. These are in addition to those in Ballymena. Your ancestors might have attended any of them. The one thing they all have in common today is that none has any records for the 1700s.
By about 1800, there were around 100 Presbyterian churches in Co. Antrim. Unfortunately due to negligence, fire and other factors, only 8 in the whole county still have records for the 1700s (and many of those are incomplete).
I don’t want to sound unduly pessimistic but for one reason and another the vast majority of Presbyterian church records in Ireland for the 1700s have been lost. There are simply no records to consult and so it’s just not possible to trace most emigrants from that era.
I realise now that your family were part of the Rev Wm Martin’s group of emigrants. Apart from the Rev Martin himself, whose origins in Ireland and training in Scotland, are recorded, I have never heard of any of the emigrants descendants being able to trace their families in Ireland with any certainty. A lot of people have tried but the records just don’t exist. Sorry if that sounds pessimistic.