The Fullriver 402222(s) is 21 x 21.5 x 3.9 mm. This is currently the closest thing I can find on the market. http://www.bsdmicrorc.com/index.php?show...
It is the same manufacturer as far as I can tell and I believe its basically the same battery. I think the measurement discrepancy is due probably to the flaps that LiPo batteries have. Either way, this is the website that I got sent to by Fullriver when I contacted them to see where I might be able to purchase their batteries in the US seeing as I couldn't immediately find them.
The obvious problem here is that it doesnt come with the ribbon soldered on it. You would have to desolder the battery assembly from the pebble, desolder the ribbon carefully from the bare cell, then reverse that with the fresh cell. And thats assuming your problem is the cell itself and not something on the assembly.
It is possible with heat and a ton of patients. Took a buddy of mine a whole afternoon to open it. Once he had the connector reseated, he actually used a of some sort to hold it in place instead so he wouldn't have to have the whole Pebble stuffed. Then he used the same putty/glue to help seal the watch shut. I'll see if he'll tell me what it was.