I'm not sure how much power is drawn by the C4s with phantom... The website says <2ma, but I doubt that...
Here's the stuff: Typical 9v batteries have a capacity of about 500mAh, or 500 milliAmp-hours. The 9v WalMart battery is 5400mAh, or almost 11times the capacity of a single 9v battery.
Hypothetically, if 1000mAh (2x akaline 9v batteries) runs your mics for 4 hours, the mics have a draw of 250mA per hour. That means, if you use a battery with 5400mAh capacity, you can power the mics for 21.6 hours.
However, the ARTII has a 12v DC power input, so I'm not sure if you'll be able to use an external 9v battery...
I've also seen info that the ART II doesn't provide a full 48v Phantom, so right off the bat you'll have issues...
http://www.core-sound.com/2Phant/3.php Of course, that info is on the Core Sound site, so take it with a grain of salt...
I think you'll be OK if you move to a Denecke PS2...
Terry