If you want to run your LibraryBox from battery, in order to make it mobile, any battery pack with a USB port will power the MR3020, it's just a matter of how long you want it to run. The MR3040 has a built in battery that will last 5-8 hours depending on use, and can also be powered by an external battery. In my tests, a 6600 mAh battery pack designed for the iPad ran my LibraryBox for over 15 hours.
Given my entirely unscientific tests, the run time above means that LibraryBox draws about .4 watts. Given that, here's a chart of approximate runtimes for a variety of the most popular rechargeable battery packs.
|Capacity in mAh
|PowerGen Mobile Juice Pack
|Monoprice External Battery Pack
Solar power is highly dependent on location, and where the solar panels are, their angle, and how clean they are kept are all factors in how well a solar setup could work. Here are a few solutions, ranging from dead simple to moderately complex.
One way to go would be to try an out-of-the-box solar system designed for USB devices, like the Instapark 10 Watt Solar Panel Portable Solar Charger. It's cheap as these things go, but as it's designed to be portable I'm not sure how well it would work as a fixed installation. But for "take your LibraryBox to Bonnaroo" off-the-grid action, it might be a very nice solution.
There is another out-of-the-box option for this, based around the Revive Solar Restore XL combined with the add-on solar panel extensions. The Restore XL is a 4000 mAh battery, and according to the Amazon spec sheet the add-on panels will recharge the battery with 4.5 hours of direct sunlight. Since the 4000 mAh should give you about 9 hours of runtime for the MR3020, as long as you can get better than 50% direct sunlight you should stay ahead of the power curve. For under $100, it's got potential as a solution.
Another option would be to design a system based around the common 12 volt battery, and build a system to charge, and then to step the voltage down to 5V USB. Something like the Instapark 10W Mono-crystalline Solar Panel with 12V Solar Charge Controller, combined with some cheap 12 Volt batteries and a 12 Volt to 5 Volt convertor designed for motorcycle use should work. All together, it's not much more expensive than the above options, and is far more powerful.
I have not tried any of the solar solutions above...these are just first-blush guesses at what might work. If you are interested in this sort of LibraryBox installation, please let me know, I'd love to know what you're planning!