This is what I was sent by Stone Mountain Park person:

According to the Park's Ordinance 8-106 - Pets and Other Animals:

No pets other than dogs and cats are allowed in the Park.

Pets must be kept at all times on a leash not exceeding six feet in length. The person having custody or control of such animal is responsible for the removal of pet waste.

Pets are NOT permitted in the following areas of the Park: Beach and bathing areas; lakes; golf course; all buildings; hiking/nature trails; anywhere on the surface of the mountain within the perimeter of the railroad track surrounding the mountain including the walk-up trail to the top of the mountain; attractions; Memorial Lawn; Laser Show; at special events; or in any other area with signs posted prohibiting pets.

Pets cannot be left unattended and/or locked in a closed vehicle between the dates of May 1 and September 30.

Pets are allowed at the Campground if kept on a leash.