“there is no dialect in America… unless some scanty remains of the croaking, guttural idioms of the Dutch, still observable in New York; the Scotch-Irish as it used to be called, in some of the back settlers of the Middle States …"
– Boucher’s Glossary of Archaic and Provincial Words, 1832.
The Glossary was published posthumously. Boucher (1738–1804) was an Anglican clergyman, a close friend of George Washington, and lived in America from 1768–75.
His Wikipedia entry is here.
Further south, down in the Carolinas, this famous quote from another Anglican clergyman, Charles Woodmason, appeared in 1767:
This is a very fruitful fine spot, through which the dividing line between North and South Carolina runs — The heads of P.D. River, Lynch’s Creek, and many other creeks take their rise in this quarter, so that finer body of land is no where to be seen, but it is occupied by a set of the most lowest vilest crew breathing Scotch Irish Presbyterians from the North of Ireland — They have built a meeting house and have a pastor a Scots man among them — A good sort of man — He once was of the Church of England, and solicited for orders, but was refused — whereon he went to Pennsylvania, and got ordained by the Presbytery there, who allow him a stipend to preach to these people, who (in his breast) he heartily contemns — They will no suffer him to use the Lord’s Prayer. He wants to introduce Watts’ Psalms in place of the barbarous Scotch version — but they will not admit it
Further early uses of the term Scotch-Irish can be found here