Hi Karana,
You are right that used car batteries are not very good for these projects. They tend to have failed, just like the rest of the vehicle as it arrived at the junkyard. And the other issue of having kids handling these batteries with liquid acids inside is probably the best reason to stay away from them.
Other things you might use...
There are some kinds of power tools that are battery powered (drills, saws, etc.) and these are a great resource for batteries. Flashlights, clocks, children's toys... there are varieties that have rechargeable batteries and some that don't. Maybe you could find portable land-line phones (but not sure if they were ever popular in the IC!)
Kind-of obvious but old cell phones also have batteries and the phone may be disposed before the battery expires. You have to deal with the infinite variety of terminals to connect a group of them together, so any given group should be matched. Some of these tasks the kids can help with, depending on age and skill, of course, as you probably know well.
Will you be teaching the kids skills like electric measurements, soldering, etc.? What ages are involved?