I have put quite a lot of thought into this myself, and hope more people jump in with ideas.
So far the best I can come up with is... (Not sure if its a good idea)
Solar, wind, or hydro charging the batteries.
A dump load controller with a timed dump, like Chris G's Homepower circuit, but set to a much longer dump time. Maybe 3 minutes?
The dump load is an inverter. The compressor is pluged into the inverter.
The batteries get full, the compressor comes on. The batteries should have a long life because they are almost always full. And if the pressure gets low while the sun is not out, it can be switched on to add pressure.
I have a feeling very large air and water tanks are a good idea.
DC compressors are either VERY expensive, or junk toy tire pumps.
Small AC oiled compressors that will last don't seem to be made.
That leaves me thinking refridgerator compressor. I don't know about them and there isn't a lot of info floating around. I guess there are 3 kinds, but only 1 is good for an air compressor.
Best guesses... They don't take a whole lot of power, but only move 0.5CFM at about any reasonable pressure. Should move 0.5CFM at 125PSI with 150W, maybe less???.
Possible troubles, they may run hotter with a cheaper inverter, and they need a large upright pipe with baffles at the air output to let the oil cycle back into the compressor.
Two pop-offs would be a good idea, I was told 'fridge compressors can pass 300PSI easy.
Very rough math (nowhere to really start), I get a 50W PV with 2 hours of insolation will move 110 gallons of water per day. As long as the system doesn't need opened and repressurized. Double the PV watts, double the water.
G-