The most widespread, rapidly-grown and easily-grown source of biomass to produce such batteries is sugarcane itself. Much less impact than say: corn or other mainstay crops, although, algae growth is likely the next step in producing more cost-effective, safe biofuels that reduce the impact on our world. Plus, the byproduct of sugarcane is easily amassed as well. The only trouble with it is that it would have a direct price impact on sugarcane. Hopefully algae can make up for that.
Another thing to note: Self-repairing batteries would be a far better alternative to our current li-ion batteries, as the current ones simply destroy themselves with use.