Use a 9 volt battery for the supply and a 10K pot in series with it and you can adjust the resistance to give you whatever current you are looking for. (You might want to also put a 150 ohm resistor in series along with the pot so that you don't put the resistance at 0 ohms and send too much current to the mic.) I'd leave it that way, but you could find what resistance works for you and replace it with a resistor of that value. From what I have read, I think typical operating currents for carbon mic's may have been around 20mA or so. Instructions often say (as it does with the Shure mic) that the current to carbon mic's can be up to 100mA without damage. I have found that when the current is high like 50-100mA that the level is quite hot to go into a mic pre. I have also found that the sound does not really change weather you are operating at 50mA or .5mA, so you might as well choose a lower operating current that works well with your mic pre gain setup.
The capacitor I believe I used was a polypropylene 10uF.
Think of supplying the power first. Connect the battery to the resistor and the carbon mic terminals to get the current and then connect the output cable to the capacitor and the mic terminals.
There is some more info in this thread.
http://www.groupdiy.com/index.php?topic=43727.msg546124#msg546124
Hope this helps.