It all popularly began with this book by Washington Irving:
A history of New York, from the beginning of the world to the end of the Dutch dynasty, Containing among many surprising and curious matters, the unutterable ponderings of Walter the Doubter, the diasastrous projects of William the Testy, and the chivalric achievments (sic) of Peter the Headstrong, the three Dutch governors of New Amsterdam; being the only authentic history of the times that ever hath been, or ever will be published.
by Diedrich Knickerbocker
New York: Published by Inskeep & Bradford
However, what about the cartoon Father Knickerbocker? The name "Father Knickerbocker" doesn't show up in the full-text New York Times database until 1891!
The book by the late Irving Lewis Allen, The City in Slang: New York Life and Popular Speech (1993), mentions neither "Father Knickerbocker" nor even "Knickerbocker."
The Daily Graphic (NY) has some of the best and earliest cartoons.
4 October 1873, The Daily Graphic (NY), pg. 665:
24 October 1873, The Daily Graphic (NY), pg. 801:
OUR LOCAL POLITICIANS SHEARING FATHER KNICKERBOCKER'S LITTLE SHEEP.
28 October 1873, The Daily Graphic (NY), pg. 825:
FATHER KNICKERBOCKER AS MACBETH.
18 November 1873, The Daily Graphic (NY), pg. 113:
FATHER KNICKERBOCKER GIVES A MAGIC LANTERN HINT TO THE COMMON COUNCIL OF WHAT MIGHT HAPPEN.
21 March 1878, Defiance (Ohio) Democrat, pg. 7, col. 1:
The New York Graphic cartoonist paints Father Knickerbocker as he makes this speech to the Gotham office-holder: "See here! You're a pretty set of fellows! How dare you cut down the $500 salary of this poor girl who teaches your children, while your Sheriff helps himself to $100,000 a year, your Register to $60,000, your Coroner to $25,000 and your County Clerk to $50,000? And this is what you call economy?"
A search for "Knickerbocker" in the New York Public Library catalog turns up this as the earliest:
An act to incorporate the Mutual Assurance Company, of the City of New-York. Passed the 23d day of March, 1798. Together with the bye-laws, rules and regulations, for managing the affairs of said company.
By the Knickerbocker Fire Insurance Company of New York
New-York: Printed by James Oram