With the STC counter chip in the PCI-MIO-16E-4, you will not be able to configure it to return a zero if no pulses come in on the Source, it will always return the current value of the counter.
What you will want to do is set up a simple loop that will check every value of the array to the previous value. If both values are the same, change the second one to zero.
Let me know if you have any problems implementing this.
Brian