I have come across this family before. Perhaps a couple of years ago. I vaguely recall taking a couple of ladies from Canada to Layd Old graveyard to look for the grave, as well as to the house in Tavnaghoney where Mary died in 1903. This is her in the 1901 census (married name McAllister).
http://www.census.nationalarchives.ie/pages/1901/Antrim/Cushendall/Taunaghoney/923305/
Her husband’s death in 1891:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1891/06057/4726497.pdf
The tithe applotment records for 1826 list a Duncan (Dunkin/Dunken) McIlherin in Tavanahan and also in Tavanagh/Brack/One/Norkat. The name Duncan is not very common there. That’s got to be connected to your family.
http://www.irishgenealogyhub.com/antrim/tithe-applotments/layd-parish.php
It’s quite confusing. There’s Tavnaghoney, Tavnaghbrack and Tavnaghowen (spelling varies for all) and they are all very close to each other. Tavnaghbrack will be the Tavanagh/Brack in the tithes. I recall looking at Tavnaghbrack with the 2 ladies for the likely location of the farm there, just off the modern Tavnaghan Lane. Whilst we were there a local farmer named McDonnell appeared and chatted to us but could add nothing to our knowledge. It was all too long ago.
You mention Layd Church of Ireland graveyard in Ballymena. Layd is nowhere near Ballymena. It’s about 20 miles away from Ballymena, on the coast overlooking the Irish Sea. There are several graveyards in Layd. My recollection is that your family are in the Old graveyard, halfway up the hill road towards Cushendun. It’s steep and slippery in the graveyard at times. Take care if visiting.
Incidentally, according to MacLysaght’s “The Surnames of Ireland” McIlheron/McElheron is a sept of the Scottish McDonnell/MacDonald clan. So your ancestors probably originated in Islay, Gigha or Kintyre or one of the other MacDonald lands in that part of Scotland. They likely moved to Ireland in the 1500s or 1600s when the MacDonalds established themselves in that part of Antrim. (Half the population of the Glens have the same broad origins). In 1654 a Dutch traveller in Scotland commented: “Today in the Irish language, which is in use over this whole area, it is called Kintyre, that is Head of Land. It is inhabited by the family of Mac-Conell, which has lordship here but at the pleasure of the Earl of Argyll; they regularly go off to Ireland for booty in their light ships, and have occupied the small provinces called Glen and An Rara/The Route.” (Source Joan Blaeu “Cantire in Atlas” Amsterdam 1654 page 58).
The MacAllisters also originate in Scotland. They arrived in the Glens of Antrim in the 1600s after some unpleasantness with the Campbell clan at the bottom end of Kintyre (which is about 11 miles away). A few severed heads. That sort of thing.