Is there anyway to use a battery, rechargeable preferably. Is there anyway or any battery packs?

You can always connect 12V/7Ah battery like this (see below)
Carambola consumes 1.5W, it is 0.125A at 12V. So with this battery it (theoretically) should be alive for 56 hours, which is more than two days.

Nothing smaller that could be handheld?

First you should ask yourself how long do you need to be running on battery. Lets say you need 3 hours. Lets assume you have 12V battery. Carambola alone consumes 0.125A of current at 12V (12V * 0.125A = 1.5W). So you need battery with capacity 3h * 0.125A = 0.375Ah. Which is theoretical. In general multiply this number by 2 to be sure. So 0.75Ah battery should be fine. There can be used almost any charging circuitry.

What sort of connections would it be?

Sorry, I don't understand what you need.

I need something that will last about 3 hours, a lightweight fairly small battery pack.

For instance you can use this battery: http://www.hobbyking.com/hobbyking/stor ... _Pack.html. Just keep in mind that LiPo batteries can't be discharged completely. Also you should buy charger together with this battery.

Would that plug straight into the carambola development board?