Hi,
Try this place.
http://www.batteriesplus.com/You might be better off buying a 1800 watt UPS system, on sale, and then take out the battery from it. Normally they run on 12 VDC, and would work. The problem is that most batteries are 9" to 12" tall, and it does not look like you have that much space. A pair of 25 AH emergency light batteries, or other small batteries might be your best thing.
You really don't need a battery charger, just a 30 amp fog light relay under the hood that is energized at all times when the ACC position is on, or the radio is getting power, then it will turn on. Connect one side to either the alternator output (for higher voltage) or the battery +12 terminal (about 0.8 volts less) then go to a 20 amp fuse, then to the new batteries. They will run from the alternator while the engine is on, and battery when the engine is off.
Then install a couple of cigarette lighter receptacles to plug in whatever. You can wire the inverter directly to the battery too - use a 20 -30 amp fuse.
This battery is only about 7" tall.
http://www.trojanbattery.com/product/12-agm/Fred.
