I get my batteries at a place that sells mototbike, quads, gardening equiptment, outboard engines etc. They aren't car batteries no, not sure if they put them in motorbikes eithe rbut thye stock them here. I have known guys who have carried car batteries though!
Just make sure the battery you get is a "sealed lead acid" one which is rechargeable, you definately don't want one to leak all over you. Easiest way I have found to carry them is to put them into a small backpack that has good wide shoulder straps, that distributes the weight nicely.