There are a few Suffolk County parks that have camping in the Hamptons. Check out the link below. Look under Eastern Suffolk County. The ones I listed below all have camping. A few are VERY hard to get into (the two with "beach in the names). Your going to have to search on the site or make some phone calls. The parks are for residents with a "green key". Im not sure how the reservation system works for people living out of state.
Suffolk County makes it very hard for non residents to camp in the county parks, when all is said and done non county residents end up spending almost 35 if not more a night.