The only way to get on to Pirates Lair (formerly known as Tom Sawyer Island) is by CM guided raft (unless you are a very good swimmer and plan to have your last visit to DL ) I don't know of any specific time; its more like luck of the draw; but even if you miss one another will be along in a few minutes.
The rafts are on the tail end of the Rivers. The rafts travel back and forth pretty quickly. I believe that you only have to wait a couple of minutes. I hope you have an awesome time because Tom Sawyer Island was taken over by pirates !