The earliest use of the term that I have seen was in estate inventories in Jefferson County, Tennessee Ca. 1800-1810 where a "shot gun" was among the items on the inventories along with "rifle gun","shot pouch", and "wipers". Note that the term shot gun was comprised of two words.There are also the the account books of Leonard Reedy {1774-1837} a gunsmith of Dauphin County,Pa.who worked from about 1792 until his death in 1837.There are two account books in existent covering the period from 1819 to 1837.They are in German and English with German being the earlier.He refers to guns,rifles,a smooth rifle,a shotgun,and a double barreled rifle.The entry for the shotgun was made in 1828.he also recorded entries for gun restocking and repair as well as general repair for other items.He restocked 31 guns and charged from $2.00 t0 $4.75.These accounts also show the 18th century terminology for gun parts as well as fascinating picture of an early 19th century gunsmith/blacksmith who was also a jack of all trades.
"Thoughts on the Kentucky Rifle in it's Golden Age" by Joe Kindig Jr.PP.13-22