The VoCore by itself, with the WiFi operating will draw 260mA via USB, so that's 1.3W. The power output of the original solar panel on the rock is probably too low to keep the VoCore running, so an upgrade is in order. I'm thinking something like the Adafruit USB / DC / Solar charging module. This needs a 6V solar panel, so I have a few options:

1. Sacrifice several solar garden lights to get the required power level (up to $15 depending on quality)

2. Make a solar panel from bare cells  (cheap if you don't want weather protection.....)

3. Buy a suitable panel with the charging module ( $25)

4. Use a solar panel from an LED shed light, as these look to be the right size (I'm going to have to go to Bunnings and check them out) ($20+)

As for the battery - I'll find a cheap small single cell LiPo around somewhere. Cost is under $10 from somewhere like HobbyKing.

So for a 2000mAh battery, I might get about 6 hours of usage from a single charge. I should probably aim for a non-stop-rock, so a 5000mAh capacity battery might keep the rock up all night. Something like this maybe? I really only want to plug the rock into a USB  socket in case of emergency, unlike some rocks that need a constant connection...