I ran my AD1000 off an Electrovaya PowerPad 160 (15-16V Battery). I built a Voltage Regulator that would regulate the battery output down to 12 volts.
The PP160 weighs around 2 lbs and would run at about the equivilant of a 10AH 12V SLA with my setup. I put this setup together back in early 2002.
They are kind of pricey at about $300 online nowadays - I paid well over $500 for mine in 2002 (Ouch!!!) but I am still using it today without issue with my SD702 (and no regulator is required).
Nowadays, you should be able to use one of the battery geek batteries, such as a 10-14-88 (should run pretty close to a 7.2 12V SLA - the typical Eco-Charge size - or run the AD1K for about 4-5 hours)
http://www.batterygeek.net/Portable_DVD_Player_Battery_p/10-14-88_batterygeek.htmWeighs about 2 lbs.
War Eagle!