DC Air pump oscillator - square vs sine
I'm imagining this to be a low-volume reciprocating pump like those used for aerating aquariums? 

If so then you may be better off just replacing the air pump with one that uses a 12V DC motor. These are commonly available, such as here http://www.robotshop.com/en/sfe-air-pump.html and http://www.ebay.com/itm/12V-DC-micro-Diaphragm-Drain-pump-Pumping-air-pump-for-aquarium-drinking-water-/171122685480?pt=LH_DefaultDomain_0&amp;hash=item27d7b4f628.