The Rules for camping in the Catskills:
No camping within 150 feet of any road, trail, spring, stream, or other bodies of water except in camping areas designated by the DEC.
You don't have to bail on the Catskills, if you follow these rules, there are spots where you could park at a trailhead and search out a flat area 200 feet from the road & trail.
This option of course would not have the luxuries of car camping.
There are a few trailheads which begin on private land though, one of which is the Devils Path eastern Terminus.
Just make sure the trailhead and trail you will be camping off of is in a green section of the map (NYS Forest / Wilderness) I assume you will have a NY/NJ trail conference map of the area, the only map to have for the Catskills. Oh and a flatter area would help, for instance, the Roaring Kill Trail off of Elka Park Road with acess to some great peaks, actually this is the area I would reccomend for your situation.