If you call the Harbormaster Stephan Land on VHF 12 They will let you know if there are any private moorings available. They usually ask you to call after 3 p.m. So if you get there earlier, just anchor and wait until 3. Though, you could always try them earlier....No guarantees that they'll have one, so pick an anchorage that you're prepared to spend the night on.
They're not free, they're "supposed" to collect a fee, and to my knowledge they are only good for one night.
The other strategy if you want a green town ball, is to get up early and take the dinghy through the mooring field to see if anyone is leaving. Attach the dinghy and call the mothership..;-) on a handheld or walkie talkie.