Miller/McCarter

The family is listed in the 1851 census for Ballyhackett. It includes the information that John Miller (farmer) died in 1847 of a fever.

http://www.census.nationalarchives.ie/pages/1851/Antrim/Upper_Glenarm/Carncastle/Ballyhackett/6/

There are no Millers listed in Griffiths Valuation in 1861 so that seems to point to the family leaving Ireland between 1851 and 1861.

You don’t say what denomination the family were though the most common denomination in that area is Presbyterian. If so then unfortunately their earliest records start in 1833, so there may not be a record of John & Jane’s marriage, or the baptisms  of most of their children, save for Jane who was evidently born c 1843. There’s a copy of the Carncastle Presbyterian records in PRONI (the public record office) in Belfast. A personal visit is required to view them.

John Miller is listed in the tithe applotment records for Ballyhackett in 1834. You would be able to find the size of his farm from the more detailed records held in PRONI. That in turn might help you locate the farm today, should you ever wish to do so. There were only 6 farms in the townland in 1861 and so it may not be too hard to find John’s.

Sorry I did not see the 2019 reply. Here’s a link to the 1834 tithes in Carncastle. They list John Miller in Ballyhackett:

http://www.irishgenealogyhub.com/antrim/tithe-applotments/carncastle-parish.php

They are also on the PRONI website where the exact size of the farm should also be listed. The measurements will be in Cunningham acres (a measure popular in Scotland and the north of England). Multiply by 1.62 to get standard statute acres.

If you go to Ballyhackett on the Griffiths site 

http://www.askaboutireland.ie/griffith-valuation/index.xml

you will see that in 1861 there were 6 farms (though two of them were rented by the same person). Thomas Shaw had approximately 41 acres, Henry Shaw had 59 & 142, Robert Stewart 44, Rev Carmichael 33 & John Barber 19. (These measurements are statute).  What you may be able to do is compare who was renting in 1834 with the names in 1861. That may tell you which farms have not changed hands and so can be excluded. You might also be able to work it out by comparing the acreage (converting the tithe acreages by multiplying by 1.62). That’s not an exact science because of course people acquired and lost land, so it’s not guaranteed they are all exactly the same 30 years later. But it might help. The farm occupied by the Rev Carmichael is probably “Church farm” which is beside the Church of Ireland. You can probably exclude it as it will be part of the church’s property and occupied by the incumbent.  The farms are all on either Sallagh Rd or Ballymullock Rd, just south of Cairncastle. There are maps in PRONI and in Ballymena library which show the exact locations of each of the Griffiths farms, so if you can pinpoint a specific farm, then you could narrow it a bit further. (Though both the library & PRONI are closed at present).  But that said, they are all on either Sallagh or Ballymullock Rds.

From general experience, it’s unlikely that the current occupants of these farms will all know who lived there in the 1840s. 

With regard to where the family might be buried, I do not know if either of the 2 Presbyterian churches has a graveyard, but if they do, try there. Failing that try Cairncastle Church of Ireland.  It’s far from guaranteed that there will be a gravestone. Not everyone could afford one.