One possible solution would require the use of two counters. The first counter would be set for Simple Event Counting. You would need to set the initial count to 1 and set it to count down and set the output to toggle on the terminal count. Apply your trigger to the source of this counter. After the first pulse, start trigger, comes in, the counter will count down to zero, TC, this will toggle the output high. Then when the second pulse, stop trigger, comes in, the counter will count down to 2^24-1, which is not the terminal count, so the output will toggle back to low. What this basically does is generate a high signal between the start and stop trigger.
You would set up the second counter for pulse train generation and set the frequency to the rate you want
to acquire data. This pulse train will be used as an external clock for the acquistion. Route the output of the first counter to the Gate of this counter. (This can be done internally.) What this will do is generate a pulse train when the output of counter 1 is high. (between the two pulses.)
Brian