I've used DVD batteries and RC car batteries. Either will run for a long time.
Last year I used 2 RC car batteries to run a PS2/AD20 combo at the side stage of a weekend festival... checked them with a volt meter before starting and the "9.6V" battery said something like 10.4. I started it running at noon, let it run all day and all night... there was a show which ran like midnight - 4am... I hit record at midnight and went to bed, letting the rig run overnight. When I came back in the morning, the voltmeter... it wasn't even down to 9.6v yet. Somewhere along the way I did swap the batteries with each other... in other words moved the AD20 battery to the PS-2 and vice versa... I think the PS-2 uses more than the AD-20. But the point is that you can easily get 24 hours use from a RC car battery, maybe 2 or 3 days, I'm not sure.
Making up a cable isn't rocket science... buy 2 RC car batteries at walmart, comes with 2 chargers. Each battery and charger has a white connector on it. Use the connector and 6 or 12" of cable off one of the chargers, wire that connector up to a 1/8" mono-miniplug from radio shack. Red wire goes to the middle. Like everyone else has said, plug the mini-jack into the AD20 first. Might as well tape it in place and forget about it. Then connect the white connectors.