I was looking for a Li-ion power source adapter and found this in the process.
Looks like it would serve as a UPS for a rPi in many situations. The listing isn't big on specs, but they seem to show it will drive well over an amp in a pass through mode. They talk about a couple of amps on each of two ports in power bank mode.
I know this has been kicked around a bit here, but I don't know if anyone found an economical solution. This unit is around $10 and a Lithium battery will cost around another $4 or $5. You can either use the standard 18650 type or one of the Lithium polymer flat cells. Both seem to be available cheaply with about 3000 mAHr capacity running a typical pi for around 2 hours.