The Fatty Stabalizer is made for low pressure application. Unless your CO2 tank has a primary regulator attached, and I doubt it does, use the regular Stabalizer.
All Palmer's regs are "omni-gas ready." So yes, you can use it with CO2. Just make sure that your marker operates on low pressure as this regulator is only adjustable from 0-400psi.
Edit: I don't know why you would need a primary regulator on your CO2 tank either. An anti-siphon would help though.