Iowa Tinkerer,
Because the digital lines on the PCI-6602 are PFI lines, you should be able to route DIO_0 (PFI_0) to the Start Trigger for your counters. First, you will use the GPCTR_Change_Parameter() function to enable the Start Trigger for each of your counters. Then, you will use the Select_Signal() function to route PFI_0 to the Start Trigger. This should do the trick.
Good luck with your application.
Spencer S.