Shade is a very important consideration for all playgrounds, but especially in warmer climates. As you mentioned, large shade structures over the playground provide the best cover, but are also extremely expensive. Another option is to work with the playground designer when you're planning a new playground so that they incorporate as many shade roofs as possible actually on the structure. While some surfaces will still get hot, the majority of the playground would still be safe to play on. It's also worth thinking about what type of materials you're using, and trying to stay away from as many mental surfaces as possible.
The last, and arguably best, option is to either install the playground near existing trees that provide shade, or to plant numerous trees around the playground once it has already been installed. Work with a professional arborist to determine which trees will provide the most shade, which will fare the best in your climate, and how they will grow. Keep in mind that you'll need 7 feet between the play surface and any shade to ensure that things stay safe!