Judy,
There is 1 Daniel McClarty listed in Layd townland in Griffiths Valuation for 1861. He had plot 10 which was a 20 acre farm. There were other McClarty households nearby who were presumably related to him.
The Valuation revision records show Daniel’s name against that property till 1885 when he is replaced by James (suggesting Daniel may have died). I searched the statutory death records and there is one for Daniel on 4.2.1883 aged 81.
The informant was his son James:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1883/06378/4830443.pdf
This looks to be James in 1911 with his wife Mary Ann Bray:
http://www.census.nationalarchives.ie/pages/1911/Antrim/Cushendall/Layd…
The McClarty families in Layd in the 1901 & 1911 censuses all appear to be Church of Ireland. Layd Church of Ireland has records from 1826. There’s a copy in PRONI in Belfast. The records are also on the rootsireland site. There is a record of James birth to Daniel & Mary McClarty on 26.1.1849 in Layde.
Daniel's wife Mary died 28.2.1884 at Layde. James again was the informant.
James evidently died in 1932. His will should be in PRONI in paper format.
McClarty James of Layd county Antrim farmer died 23 March 1932 Probate Belfast 29 June to Mary Ann McClarty the widow and Daniel McAllister auctioneer. Effects £40.
James McLarty had married Mary Ann Bray on 18.3.1886 in Cushendall, Church of Ireland. She was from Strangford (Co. Down) and her father John was a seaman.
The family rented from the Antrim Estates. Their tenant records are held in PRONI in Belfast and go back to the 1820s. So you could probably confirm Daniel’s presence on that farm back to that period. He is listed in the tithes for 1826, so he was farming in Layd then:
http://www.irishgenealogyhub.com/antrim/tithe-applotments/layd-parish.p…
Getting back much before the start of the church records may prove challenging.