You will need either a pure sine inverter (12v to 120v) to run the c-pap when off-shore power (no hook-ups) or you will need to buy a 12v powered c-pap, called a travel c-pap.
A portable travel c-pap will probably need recharging after each overnight use...however some units have multiple battery and charging options.
Here is one place to begin your search:
If you decide to keep using your existing c-pap and install an inverter in the r-pod, do not cheap out on a modified sine wave inverter for $50. You will need a good high quality inverter, it will be powering medical equipment after all. Depending on your particular c-pap, normally they can be powered by a good 300-500 watt pure sine wave (PSW) inverter. Expect to pay around $150-$300 for a decent one.
If you post the label ratings (volts, plus either watts or amps) we should be able to narrow it down.