The Belfast Commercial Chronicle of 16th November 1836 has an advert:
“Lime Works. To be let, from the 1st November next, for such term as may be agreed upon, The Lime Quarries, Kilns, and Turbary of the Lime Works of Moyaver the property of George Macartney Esq, as now in possession of James Ferguson. A deposit of two years rent as security will be required. Apply to Charles Douglas Esq, who will receive proposals for the whole, or for the quarries separately from the kilns and turf banks. Dervock June 290 1836.”
The Macartney papers are in PRONI (D1062/2). You might find more about the quarry there.