Here is the datasheet and app notes for building a constant current source.
Your approach to using a 9V battery and a series resistor is not a constant current source- your current will change as the battery's voltage drops and the current will also change with changing load resistance. But regardless, you should have been able to measure some voltage across your resistor under test. Are you sure your connections were correct?
1mA * 2Kohm will yield 2V
Let us know if you need further help, good luck!
I am not familiar with VI Logger nor the 6008, but it should not matter what analog input channel you use to measure the voltage drop across the resistor under test. All I can suggest is make sure the anaolog input channel used is set to differential mode, if that is possible with your SW and HW.
The most direct off-the-shelf approach I can think of is to use one of NI's DMM products such as the NI 4060: