The reason you are getting the routing error with the 6534 is that you can't route the timebase to the digital output sample clock. If you look in the Measurement and Automation Explorer under the Device Routes tab (click on the device you want to see the routes). This mapping shows that the 20MHz Timebase does not route to the DO Sample clock.
If you want to count edges using the 6602 you would use CO channels instead of DO. There are some examples of how to set up CO lines in C:\Program Files\National Instruments\NI-DAQ\Examples\DAQmx ANSI C\Counter. Usually you can do a finite buffered event counter, but I had some issues with the 6602 routing. If you have an M Series board, it is a lot easier. I hope this helps explain the errors that you are getting. Have a great day!
You are absolutely right, I must have been looking at the device routes incorrectly. If you want to to use the PCI-6534 20MHz signal for the time and the PCI-6602 for the counting, try the following:
1. Export your 20 MHz Timebase from your PCI-6534 to a PFI line or RTSI line using DAQmxSetExported20MHzTimebaseOutputTerm(TaskHandle taskHandle, const char *data);
2. Use the example Cnt-Buf-Cont-ExtClk (C:\Program Files\National Instruments\NI-DAQ\Examples\DAQmx ANSI C\Counter\Count Digital Events\Cnt-Buf-Cont-ExtClk) to read in your counts every second, based off of the external clock that you exported to a PFI line in step 1.
NOTE: There is a 20MHz Timebase on your PCI-6602 as well. Have a great day!