The Synplify Pro Synthesis Production version C-2009.06 does support CXT devices.
In some cases, Virtex-6 CXT device support is required for an unsupported synthesis tool or IP. As a work-around, you can target similar Virtex-6 LXT devices in the synthesis tool and the CORE Generator tool first, then re-target to CXT devices during design simulation, implementation, and while using the Power Estimator/Analyzer. The UCF constraints file should also be modified for the CXT device.