North Carolina is now known as the “Tar Heel State,” but in the early 19th century it was known as the “Tar and Turpentine State” (or just “Turpentine State”). The state was a major producer of turpentine.
 
“The old tar and turpentine State” was cited in a February 1832 newspaper. “The old turpentine State” was cited in a September 1836 newspaper. The ‘Turpentine State” nickname was infrequently used after 1900 and is mostly of historical interest today.
 
   

Wiktionary: Turpentine State
Etymology
A nickname alluding to its extensive production of turpentine.
Proper noun
Turpentine State
1. North Carolina
 
Wikipedia: Tar Heel
Tar Heel is a nickname applied to the U.S. state of North Carolina and its inhabitants. It is also the nickname of the University of North Carolina athletic teams, students, alumni, and fans.

The exact etymology of the nickname is unknown, but most folklore believe its roots come from the fact that tar, pitch, and turpentine created from the vast pine forests were some of North Carolina’s most important exports early in the state’s history. For a time after the Civil War, the name Tar Heel was derogatory, but it was later reappropriated by the people of North Carolina.
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History of term
In its early years as a colony, North Carolina settlements became an important source of the naval stores, tar, pitch, and turpentine, especially for the British navy. Tar and pitch were largely used to paint the bottom of wooden British ships both to seal the ship and to prevent shipworms from damaging the hull.
 
At one time, an estimated 100,000 barrels (16,000 m3) of tar and pitch were shipped annually to England. After 1824, North Carolina became the leader in the United States for naval stores. By the Civil War, North Carolina had more than 1600 turpentine distilleries, and two thirds of all turpentine in the United States came from North Carolina and one-half from the counties of Bladen and New Hanover.
 
Historians Hugh Lefler and Albert Newsome claim in North Carolina: the History of a Southern State (3rd edition, 1973) that North Carolina led the world in production of naval stores from about 1720 to 1870.
 
At the time, tar was created by piling up pine logs and burning them until hot oil seeped out from a canal. The vast production of tar from North Carolina led many, including Walt Whitman, to give the derisive nickname of “Tarboilers” to the residents of North Carolina. North Carolina was nicknamed the “Tar and Turpentine State” because of this industry.
   
(Oxford English Dictionary)
Turpentine State  n. (U.S.) see quot. 1859.
1850   M. Reid Rifle Rangers I. v. 46   The danger is, we may stick in the Turpentine State.
1859   J. R. Bartlett Dict. Americanisms (ed. 2)  Turpentine State, the State of North Carolina, so called from the quantity of turpentine obtained from its pine forests.
 
11 February 1832, Farmers’ Cabinet (Amherst, NH), pg. 1, col. 4:
Tennessee suspended the tax on cotton gins, but North Carolina, the old tar and turpentine State, stood firm, and made a special resolve, “that the contract ought to be fulfilled with punctuality and good faith.”
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B. Cour.
 
16 September 1836, Louisville (KY) Daily Journal, pg. 2, col. 2:
Then let North Carolina illuminate on account of the victory of the Whigs. Let the old turpentine State set all her tar on fire.
 
1 March 1838, Scioto Gazette (Chillicothe, OH), pg. 2, col. 1:
The honorable little Mr. Bynum, of the Turpentine State, who has such a holy horror of those “bank-fed scavengers,” ...
 
3 September 1839, Louisville (KY) Daily Journal, pg. 2, col. 2:
NORTH CAROLINA.—In recent North Carolina elections the Whigs did not obtain as many members of Congress as many of them had anticipated, yet an inspection of the popular vote shows, that the strength of the Whig party in the State, far from diminishing, is rapidly increasing, and, that there is as absolute a certainty of a Whig victory in the “old Turpentine State” in 1840, as in Kentucky or Massachusetts.
 
11 November 1842, The Daily Picayune (New Orleans, LA), “A North Carolina Joke,” pg. 2, col. 3:
North Carolina is “a place. Every body who has ever heard any thing has heard that it is called the “Old North State,” the “Rip Van Winkle State,” the “Buncombe State,” and the “Tar, pitch and turpentine State.” The river Tar is one of its most prominent and important tributaries—on the banks of which is situated the famous town of Tarborough.
         
Chronicling America
28 October 1846, The North Carolina Standard (Raleigh, NC), pg. 2, col. 4:
... and if the North Carolina boys should be called into action, we hazard nothing in saying that the banner of the “turpentine State” would be seen flushing in the thickest of the fight.
 
Google Books
January 1865, The Ohio Educational Monthly, pg. 14:
ANTONOMASIA IN GEOGRAPHY.
BY W. D. HENKLE.
Pg. 15:
... North Carolina, the “Old North State,” and “Turpentine State;” ...
 
Google Books
The Complete Compendium of Universal Knowledge
By William Ralston Balch
Philadelphia, PA: Franklin Square Bible House
1891
Pg. 370:
TURPENTINE STATE, a popular name for the State of North Carolina, which produces and exports immense quantities of turpentine.
 
Google Books
Universal Dictionary of the English Language
Edited by Robert Hunter and Charles Morris
New York, NY: Peter Fenelon Collier, Publisher
1898
Pg. 5343:
North Carolina. Old North State. The Turpentine State (from one of its principal products).
 
Google Books
Focus on American English & Culture (Second Editions)
Edited by Pierfranca Forchini
Milan: EDUCatt - Ente per il diritto allo studio universitario dell’Università Cattolica
2011
Pg. 49:
By 1844, the state (North Carolina—ed.) was being called the Tar and Turpentine State, and by 1859 just Turpentine State.