Tables and chairs are discouraged in Central Park due to the damage the legs can cause to the lawns.  There are a few wooden picnic tables scattered around the park, some are located along the East Drive on 90th street, and near the great lawn on the east and west side by 84th street, as well as the Great Hill located on the West side near 100th Street.  Picnic tables can be moved by the parks department at the last minute, so plan on bringing a blanket for your picnic.  There are no picnic tables located on any of the lawns in Central Park, i.e, sheep's meadow, great lawn etc.