With newer drivers (Catalyst 12.4 preview: OpenCL 1.2 AMD-APP (923.1)) clinfo reports that Cayman does support cl_khr_fp64, however clAmdFft still reports that the device does not support double precision.
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clAmdFft should support double precision on the Cayman card. By default, clAmdFft checks for both the cl_amd_fp64 and the cl_khr_fp64 flags. Let us see if we can reproduce your problem in our lab.
Can you attach the output of clinfo into this thread? Make sure to include all bits of information that we would need to build a similar machine to what you are testing on, such as OS, software versions for the driver and SDK, and possibly even a test program. Are you using the client program that ships with the library?
It was my error: my context included non-fp64 capable devices, even though I was only using the one specific device.