Hi John,
It may be difficult to wire up, but it is possible to measure current with your 6024E and BNC2120.
You will need to use a shunt resistor. As you may recall, Ohm's law states that V = I * R. So, I = V/R. Your DAQ board can only measure voltage. So you will need to run your current through a resistor and measure the voltage acorss it. You can then use Ohm's law to calculate the current based on the voltage read and the known resistance.
You can either do a typical voltage acquisition and do the calculation yourself, or you can use one of the example VI's that automatically calculate the current. In LabVIEW go to Help >> Find Examples >> Hardware Input and Output >> DAQmx >> Analog Measurements >> Current. There you will see current measurement examples.
Also check out the following KB:
http://digital.ni.com/public.nsf/websearch/82508CD693197EA68625629700677B70?OpenDocument
Thanks,
Sal