From this source: http://www.dec.ny.gov/docs/wildlife_pdf/deerforecastr9.pdf
Recreational hunting is a primary use for Allegany State Park, which comprises most of WMU 9S. This unit has the most public land available in western New York, being almost entirely forested with a good combination of hardwood and mixed forest. A few larger water bodies exist within this unit, including the Allegany Reservoir. Ample opportunities for hunting exist, but separate hunting permits must be secured from New York State Office of Parks, Recreation and Historic Preservation for hunting within the Park. Though a separate permit is required, the process is relatively fast and easy, so do not be discouraged. The large wooded tracts and limited road access within WMU 9S are unique in western New York and attract hunters attempting to take a deer in a more wilderness-like environment. With adequate scouting, hunters can locate travel corridors through this heavily forested, mountainous terrain. Hunting near beaver flows or near an abandoned apple orchard (a hidden treasure) can be quite productive. Locating hard mast crops can also be very useful later into the season. The population of deer in this unit remains well below the objective level, and harvests may be as affected by hunter effort within the Park as by overall population levels.
That about sums up hunting in the park. Use the maps, find the beaver meadows, hike to the top and find the hard mast ( White Oak, Red Oak, Hickoyr Nuts, Beech Nuts,...) or find the abandoned apple orchards. The entire place was logged off, so there are many old RR grades left over to follow.
The permit is no big deal, it is on line, fill it out and carry with you. https://parks.ny.gov/parks/attachments/AlleganyRedHouseArea2017-18HuntingGuidelinesPermitApplication.pdf