Even if you already have a permit, you can get up to two more. The Department of Environmental Conservation says more deer permits are available and not just downstate.
The permits are for antler-less deer only. In an effort to control population and health of the herd, each region targets a number of deer to be harvested. Some regions saw less applications than the target number, so another round of applications will be held beginning November 1.

The following Regions, broken down into Units, will offer additional permits:
Downstate regions - 1C, 3M, 3R, 3S (bowhunting-only)
Region 7 includes Madison, Onondaga and Oswego counties 7F, 7H, 7J
Regions 8 and 9 are more Rochester to Buffalo Area. 8A, 8C (bowhunting-only), 8F, 8G, 8H, 8J, 8N, 8R, 9A, 9F, and 9G

The DEC website has details on the exact area each Unit encompasses, including an interactive map showing nearby roads. Permits are on a first come-first serve basis and will only be available at licensing outlets and not available by phone, mail, or internet. The $10 application fee is waived if you have already paid it once this year.

SOURCE: Department of Environmental Conservation