Venom Nintendo Wii Wii Fit Rechargeable Battery Pack
Provides up to 8 hours of Gameplay.
Fully charged within 2 hours.
Recharges via the USB Port on the Wii.
Compatible with Wii Fit.
The same product sells at £8.99 on Amazon.
I managed to get one instore today, so I checked online and it's available just online, but free delivery plus you can get quidco.
According to instruction you can play and recharge at the same time, haven't opened yet and tried but seems a decent battery.