Try to stay away from the inverter. It is a power killer in and of itself. You take 12 V DC and burn power to turn that into 110 V AC, then burn more power to turn that back into DC.
Resmed has a battery guide that outlines how to run an S9 on battery and has power consumption and battery capacity recommendations for various configurations. It can be found at:
Fortunately, Resmed offers a 12 to 24 V DC power brick to be used in place of the standard power supply for the S9. Unfortunately, you have to use their converter brick as they have designed their power plug around their proprietary plug. I believe that the S9 and S10 cannot be hooked up directly to a 24 V DC source as the power supply has a third wire that carries a signal between the power supply and blower. Without that signal, the blower she no work. You will need to get that power brick. It can be purchased at most online suppliers indexed on the Apnea Board; information on the converter can be found at:
I have in the past run my DeVillbiss Intellipap and Respironics System One off of a 35 AH SLA battery often used to power mobility scooters (deep cycle design and much smaller than a marine Deep cycle - weighs around 25 pounds - as opposed to around 70 pounds for a 100 AH deep cycle marine battery - when camping, I would think that to be a factor). I figure conservatively that I could get almost a week out of one. For my pressures on the S9, and without heated humidification, the Resmed guide recommends a 7 AH battery for an 8 hour night - so the 35 AH should safely get me 5 nights. Those figures include a 50% safety margin. Depending on the expected length of your camping trips or access to power sources for recharging while on those trips, you may be able to bet by with a smaller lighter battery. You could also consider a passive humidification system if you really need it - IIRC both F&P and Respironics have one that you can simply install between your naked S9 blower unit and the mask.
A good charger for this kind of application is the Battery Tender by Deltran.
Please, whatever you do, do not try and rig this through an inverter. Is that a Citabria/Decathelon in the pic?