Between the two modules you mentioned, the 9375 is the more appropriate choice since it's a mixed digital I/O module and not an analog input. I have never used an AI module for a flow meter application; I suppose it's possible, but it would seem mismatched, especially since analog sampling modules are typically a little more expensive.
The 9375's digital logic ON state is specified in the datasheet as >=10V, so 9V would not be within spec, and you would probably want it slightly higher than the 10V since the input impedance ratings are +/-5% tolerance resistances. I would find a way to increase the voltage or find a more flexible module, then start building your tick count algorithm from there.