Coquina Cove at Martin Downs Apartments for rent in Palm City, FL on ForRent.com: (866) 799-9465 - Availability, pricing and special promotions subject to change daily. Surround yourself with comfort and style at Coquina Cove at Martin Downs, a luxury apartment home community in Palm City. With five unique floorplans and fabulous services and amenities, you'll find a vacation all year long.