Shell Lumber and Hardware Co. (Miami): They carry outdoor swings and gliders, including some with wood frames (like a "Seasonal Trends F12022 Log Swing and Frame Kit" made of cedar wood). They are a good local option to check for in-stock items.
Ace Hardware: While not specifically Miami, Ace Hardware stores often carry a selection of outdoor living items, including wood porch swings. It's worth checking their website or calling a local Miami Ace store.
Lowe's: Similar to Ace, Lowe's typically has a range of porch swings, including wood options. Check their online inventory for Miami stores.
MIAMI OUTDOOR FURNITURE: They have a physical location at 4251 SW 71 Ave Miami, FL. While their "Sienna Swing Sofa" shown online appears to be more modern (aluminum/rope), it's worth visiting or contacting them to see if they carry traditional wood porch swings or can source them.
2. Online Retailers with Shipping to Miami:

The Porch Swing Company: This online retailer specializes in porch swings and offers a wide variety of wood types (cedar, oak, pine, cypress) and styles. They ship across the US, so you can order and have it delivered to Miami. They have many options for various sizes and even "swing https://www.uniqsolutions.... fully assembled.