It would be hard to pin down a flintlock rifle to NY, as noted above. NY was just not rifle territory. Those who wanted rifles often got them elsewhere during the flint period. Sir William Johnson sponsored or brought some Lancaster builders to the Mohawk valley, so the story goes. But though upstate NY is chock full of antique colonial furniture and primitives, you'll find few flintlock rifles, and none of which I know that can be attributed to NY state conclusively. In contrast, Pennsylvania has produced many hundreds of collectable flintlock rifles. As noted, THE colonial gun produced in upstate NY was the Hudson Valley fowler, and THE colonial gun associated with Long Island and the NYC area was the Britiish style fowling gun.
So for a NY state rifle you are on the right track thinking of a later, percussion rifle. Lots of them were perch belly rifles. Some were quite plain.