Sidney Edwards Morse on the Scotch-Irish, 1822

Another source,  a good generation before the ‘Famine Irish’ arrived in vast numbers, showing the usage of the term Scotch-Irish, this time in a fairly academic volume entitled A New System of Modern Geography or a View of the Present State of the World (Boston, 1822). The author, Sidney Edwards Morse, was a brother of the inventor Samuel Finley Breese Morse, and the family was of Ulster descent. The book is online here. 

The Morse brothers were both born in the 1790s; their father Jedidiah Morse born in 1761 was a Congregational pastor in New England and a descendant of Armagh-born Ulsterman Rev Dr Samuel Finley, a President of Princeton College. Jedidiah had published similar stuff in 1819, again using the term ‘Scotch Irish” (source here), and even earlier in 1810 (source here) and 1802 (source here). The earliest of his publications with the term seems to be 1789 (source here), where he also describes those in North Carolina as "descendants of people from the North of Ireland, and are exceedlingly attached to the doctrines, discipline and usages of the church of Scotland. They are a regular industrious people".

The breadcrumb trail of usages of the term ‘Scotch-Irish’ seems to be now be pretty much a continuous stream from the 1718 emigration families right up into the 21st century.