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Wikipedia is at least good enough for cites:

Although referenced by Merriam-Webster dictionaries as having first appeared in 1744, the American term “Scotch-Irish” is undoubtedly older.

An affidavit of William Patent, dated March 15, 1689, in a case against a Mr. Matthew Scarbrough in Somerset County, Maryland, quotes Mr. Patent as saying he was told by Scarbrough that “...it was no more sin to kill me then to kill a dogg, or any Scotch Irish dogg...”[52]

Leyburn cites several early American uses of the term.[53]

* The earliest is a report in June 1695, by Sir Thomas Laurence, Secretary of Maryland, that “In the two counties of Dorchester and Somerset, where the Scotch-Irish are numerous, they clothe themselves by their linen and woolen manufactures.”
* In September 1723, Rev. George Ross, Rector of Immanuel Church in New Castle, Delaware, wrote in reference to their anti-Church of England stance that, “They call themselves Scotch-Irish,...and the bitterest railers against the church that ever trod upon American ground.”
* Another Church of England clergyman from Lewes, Delaware, commented in 1723 that “...great numbers of Irish (who usually call themselves Scotch-Irish) have transplanted themselves and their families from the north of Ireland.”
* During the 1740s, a Marylander was accused of having murdered the sheriff of Lancaster County, Pennsylvania, after calling the sheriff and his assistants “damned Scotch-Irish sons of bitches.”[54]

The Oxford English Dictionary says the first use of the term “Scotch-Irish” came in Pennsylvania in 1744. Its citations are:

* 1744 W. MARSHE Jrnl. 21 June in Collections of the Massachusetts Historical Society. (1801) 1st Ser. VII. 177: ‘The inhabitants [of Lancaster, Pa.] are chiefly High-Dutch, Scotch-Irish, some few English families, and unbelieving Israelites.”
* 1789 J. MORSE Amer. Geogr. 313: “[The Irish of Pennsylvania] have sometimes been called Scotch-Irish, to denote their double descent.”
* 1876 BANCROFT Hist. U.S. IV. iii. 333: “But its convenient proximity to the border counties of Pennsylvania and Virginia had been observed by Scotch-Irish Presbyterians and other bold and industrious men.”
* 1883 Harper’s Mag. Feb. 421/2: “The so-called Scotch-Irish are the descendants of the Englishmen and Lowland Scotch who began to move over to Ulster in 1611.”

In Albion’s Seed: Four British Folkways in America (America: a cultural history), historian David Hackett Fischer asserts:

Some historians describe these immigrants as “Ulster Irish” or “Northern Irish.” It is true that many sailed from the province of Ulster... part of much larger flow which drew from the lowlands of Scotland, the north of England, and every side of the Irish Sea. Many scholars call these people “Scotch-Irish.” That expression is an Americanism, rarely used in Britain and much resented by the people to whom it was attached.