Solution
The NI-9361 only supports a single task, so all the counter channels need to be on the same task. This can be done in NI MAX or in LabVIEW.
NI MAX:
You can create the NI-DAQmx Task with multiple channels as shown below.
Create New NI-DAQmx Task... >> Acquire Signals>>Counter Input >> [Select your Measurement Type] >> [select your module] >> [select your counter number].
Here is an example with a Period and Pulse Width channel types:

LabVIEW
Option 1 (recommended): You can create multiple channels for the NI-9361 directly in LabVIEW by adding channels to the same task. As a reference, you can consult the example Encoder Velocity Measurements and the NI 9361 - NI Community.
- The example can be modified according to each user's needs and measurement type (frequency measurement, period, encoder, etc). More channels can be added one after the other, as far as the same structure of the example is followed. Notice that the property "ActiveChans" is used on top of each property node to determine which channel you are configuring (as shown in the example).
Option 2 (less Recommended): Once you have your task in NI MAX, you can call the task directly in LabVIEW as in this example:
