Coon Town was reportedly the nickname for part of the Village of Lansingburgh. The name only seems to crop up in the Lansingburgh Democrat newspaper and even there only occasionally between 1848 and 1855, although many issues have not survived so it is impossible to state for certain how frequent its use might have been. From a description given in 1848, it would seem to have referred to a southern part of the Village, south of 114th or 115th Street, what had been the Village’s 1st and 2nd Wards. To understand why it was being so labeled in 1848 (if not earlier), one needs to understand what the word meant at the time:

the word coon referred to a white country person, to a sharpster or, in phrases like a pretty slick coon, to both […] the eagerness of the Whig party to identify with rural white common people led it to adopt symbols like Davy Crockett’s coonskin cap and, in the ‘log cabin and hard cider’ presidential campaign of 1840, to nail coonskins to supporters’ cabin doors and to use live coons as signs of party loyalty. Thus Whigs also became ‘coons’, especially in the speech of Democrats
Roediger, David R. The Wages of Whiteness: Race and the Making of the American Working Class. Revised Ed. NY: Verso, 1999. 98.

SPOTS ABOUT TOWN—NO. 12.

Coon Town.

This cognomen was long since applied to all that part of the village lying south of the Bank [the Bank of Lansingburgh was at the southwest corner of 114th Street and 2nd Avenue] while Lansingburgh proper occupied the intervening space between that street and Shaver town, the southern boundaries of which we described in a former number [that must have been an issue in the week of November 28th through the week of December 26th, the week of January 9th, or the week of January 23rd; no copies of those are known to have survived]. By the insuperable prowess of Jimmy Mattison, who captured a coon at the post on the corner of State and Market streets [2nd Avenue and 115th Street], that block was added to Coon town, and has so remained. It has always been celebrated for the excellent quality and quantity of coons it furnishes for the accommodation of travelers and sojourners.—Coon town was originally settled by the Dutch, while the Yankees who emigrated here almost invariably took up their residence in Shavertown.—A few of the ancient buildings are still standing, to give to the passer-by, an idea of the tastes and notions of their founders. Gradually the business of the town has been creeping to the northward, until at the present day, Coon town numbers but very few places of business in its precincts. Its soil seems well suited to the raising of federalists, a large crop of said commodity being usually gathered about the first of November of each and every year. Commercially speaking, it bears but a very small comparison with other parts of the village—politically, it is the place where coons most do burrow, and from which the large federal majorities are principally realized. There are many spots of peculiar interest in and about Coon town; we believe it was in an upper room in Holmes’ Inn, that Gill Williams was fed on “yaller-legged” chickens to induce him to deposit a federal vote, and where numbers have often passed the night prior to important elections. This part of Lansingburgh has always been celebrated in the political annals of the county, as one of the strongholds of whiggery. In its day, Coon town has furnished more and better shooting implements to the country—Caswell’s Shop—than any village north of New York; more floor coverings—Powers’, Davenport’s, and Whipple’s Oil Cloth Factories—than any place of its size in the State; more tin-pans for the farmers—Filley’s tin ware establishment, with its numerous pedlars—than any village in the land of “wooden nutmegs”; more Captains and boatmen—there is Capts. Eseek, Nicholas, William, Charles, Nathan, Stephen, and a host of others—than any other port on the river; Our Cash all comes from a corner building in Coon town, and when we “shuffle off this mortal coil,” our friends consign our remains to a narrow tenement in its southern extremity [the Lansingburgh Village Burying Ground south of 108th Street]. May peace and prosperity attend to its citizens, and may their shadows never be less.
Lansingburgh Democrat. February 24, 1848: 2 col 2.

In the olden time a sectional war raged in the ‘burgh which was waged with as much bitterness, between the contending factions, as ever characterized the contents North and South of “Mason & Dixon’s line.” At times victory perched upon the banner of the “Coon-towner’s,” and then again the star of “Shaver town,” was in the ascendant. The record does not inform us in what manner these bitter feuds had their origin, but of their existence the most indisputable evidence is afforded. As in the case of “Mason and Dixon,” here also there was a sort of imaginary line running from east to west, and woe betided the luckless wight who might venture to [at this point a microfilm technician carelessly lost some lines of text in a fold of the original newspaper] […] Even at the present day an appropriation from the village treasury for a local improvement in Adamsville is sure to be followed by an application from coon-town for a similar amount, and vice versa.
“The Olden Times.” Lansingburgh Democrat. August 9, 1855: 2 col 2.