There are some places along the beach you can rent. If you go on VRBO you may find them there. The only downside about
staying in this area is to get to the Golden Zone you will have to water taxi every time and then taxi or bus to get where your going. It just takes you a little longer to get somewhere and if you go out for the evening in Old Towne the water taxi doesn't run after 7:00 pm.
Hope this helps you out.
Get quick answers from Stone Island (Isla de las Piedras) staff and past visitors.