In his Colonial New York: A History (p 238), Professor Michael Kammen describes the growth of Presbyterianism in New York.
The years between 1745 and 1760 were years of rapid growth for the Presbyteriana - growth based upon the influx of groups quite diverse in social origin. There were Puritans from New England and Log Island, Scots-Irish immigrants from abroad, converts drifting in from the divided Dutch Reformed communities, and members such as the Livingstons from intermarriage between Scottish and Dutch families settled in the colony since the seventeenth century. Such amalgamation could not occur without strife. Pemberton's congregation in New York City, for example, had received by mid-century an influx of what Mrs Pemberton described as 'bigotted Scotch Irish Presbyterians.' When the elders and deacons suggested introducing Isaac Watts's version of the Psalms (then widely used in New England) instead if the various versions causing some confusion in New York services, they urged that anyone who objected bring the matter to Pemberton. The newcomers decided instead to organize themselves as the 'Scotch Presbyterian Society' and formally charged the minister with neglecting the Westminster catechism when he administered baptism, failing to pray at burials when so requested by the family, and permitting the singing of anthems. Although Pemberton resigned in 1753 and moved to Boston for the remainder of his career, the Presbyterians of New York grew steadily in strength and numbers anyway.
Rev Ebenezer Pemberton was born in Boston and pastored the First Presbyterian Church in New York for 26 years. During his tenure, the great revivalist George Whitefield came to the city to preach and Pemberton was the only minister to open his pulpit to him. Whitefield preached there many times and drew vast crowds. after his years in New york Pemberton returned to Boston and pastored the New Brick Church until his death in 1777.
The quote from his wife about the 'bigotted Scotch Irish' is taken from a letter she wrote in 1755. The Pemebertons were 'new light' Presbyterians whereas it seems that the Scotch-Irish were mainly 'old light. This reflects a wider theological division in Presbyterians. Both sides were very committed to their position and Mrs Pemberton regarded those who opposed her husband as bigoted. It is also noteworthy that she described them as Scotch-Irish. This is another of the early examples of the use of the term Scotch-Irish.