Referring to New Jersey simply as “Jersey” dates to at least 1705:
Elizabeth-Town in Jersey, Aug. 30. On Monday the 20 Currant, Dyed here in the Afternoon the Reverend Mr. John Harriman, Pastor of the Church in this place, Aged about 60 Years : Who the same day at a Church-Meeting told his people, that his time of departure drew near, and exhorted them to Peace and Unity one with another, and to stand fast in the Covenant that they had engaged themselves to. — The Boston News-Letter, Sept. 3–10, 1705.
Canterbury (in Connecticut) July 3. On Monday last Died here our Excellent Pastor, the Reverend Mr. Samuel Estabrooke, … he was invited to Preach the Gospel at East-Jersey, where he was highly respected and very serviceable for several years ; but having a strong Affection to New England, he never fix'd at Jersey, but chose to return to his Native Country ; — The Weekly News- Letter, July 6-13, 1727.
To be SOLD, By John Snowden, Tanner, 450 Acres of Land on a Branch of Rariton, called Black River, in Jersey ; and near 200 Acres further up in the last Indian pur chase, and Two Acres and a Half joining to Judge Leonard's Land in Princetown near the Tavern. — The Pennsylvania Gazette, Feb. 11-18, 1734-5.
The adjective did not have to wait for roadside vegetable stands:
Ran-away the 19th of this Instant August from William Hirst, of Salem Esqr. a Jersey Boy, Named John Amy about 15 years of Age, well Sett, full Leggs, short brown Hair, Ozenbrigs Jacket and Breeches, Cotton & Linen Shirt, a Cap on his head, bare-foot and bare leg'd. — The Boston Nexus-Letter, Numb. 488, from Mond. Aug. 17, to Mond. Aug. 24, 1713.
Often, there was not just one “Jersey”:
Philadelphia, Jan. 26. We hear from Burlington, that on Tuesday the 19th of this Instant, a Marriage was consummated between Edward Peitce, Esq ; Attorney Generall of the Jersies, and Mrs. Catherine Talbot, Widow of Mr. Robert Talbot, deceased : A Lady of great Merit. — The Pennsylvania Gazette, January 19-26, 1730-31.
Inhabitants of the Jerfies, men, women, and children are reckoned at about 50,000, whereof 10,000 may be reckoned a training militia. — William Douglass, A summary, historical and political, of the first planting, progressive improvements, and present state of the British settlements in North-America, Boston/London 1755.
A tax list further divides the colony into two parts: from 1674—1702, the East and West “Jersies” were under different provincial governments. Counties in the “East Jersies” were Somerset, Monmouth, Middlesex, Essex, Bergen; “West Jersies” were Cape May, Salem, Gloucester, Burlington, and Hunterdon. Morris and Trent were recently formed and had no tax information. The complete title of Douglass’ book includes “the history of the provinces and colonies of New-Hampshire, Rhode-Island, Connecticut, New-York, New-Jersies, Pennsylvania, Maryland and Virginia.”
In 1835, John James Audubon still uses a plural, though with corrected orthography:
In the Jerseys I have found the Night Herons breeding on water oaks and cedars…