Solution
The NI 9425 does not have any pull-up or pull-down/current-limiting resistors at the inputs. The only built-in protection is 30 kOhm input impedance, as per the NI 9425 Datasheet.
You should be able to apply a 24 V logic input, without the need for additional circuitry for a pull-up resistance. Also, please note that the NI 9425 has a sinking input, as shown in the "NI 9425 Circuitry" diagram from page 4 of the NI 9425 Datasheet. Please check the "Additional Information" section below for more details.