I have traced some of my ancestry back to around this area.
I know of an Archibald Hamilton b. abt. 1879.
He married Mary Mcbride in Layd parish 27 Jun 1823.
Archibald's parents were a Robert Hamilton and a Catherine McIlheran (spelling may be inaccurate), I have no other information on either, except that Robert was a farmer.
Archibald and Mary traveled to live in Campbeltown, Scotland with some of their children sometime between 1828-1861. I have found no records of exactly where they were in Antrim prior to this except that it was around Layd parish, I have heard mention that it may have been Cushendun/Cushendall.
Mary and Archibald had at least two children while in Ireland. Archibald b. abt. 1820, and James b. abt. 1828. Due to the gap in years I suspect there may have been more that I have not discovered.
If anyone has any further information on the Irish roots, I would love to hear from you.