Good Camera for Children?

[NicoleScraps]

We have six children who have seen me obsess with photography so of course, they are all interested as well. Our kids range from 5 years to 19 years in age.
We have bought at least a half dozen of those really cheap point and shoot cameras of various brands. I can't really think of the specific brands right off the top of my head, but I am sure you know what I mean. The ones that cost around $80-$100.
These types of cameras are the worst. I have yet to see one remotely "good" photo come from any of them. You might as well forget about taking photos inside with one. They are either under exposed, blurry or have a color cast. Our oldest girl took a ton of photos of a semi important event with one. I spent over a week editing them, removing cast, lightening, sharpening, and they still kind of stunk. Natural light photos at best are still just mediocre.
I need a different option for the kids. They are interested in photography but are never going to learn to take good photos unless they at least have semi decent equipment to work with.
So I was thinking about buying several used or refurbished older cameras. Maybe 3-5 years old but in their time, were top of the line point and shoot cameras. But are now cheap because the manufactuer has came out with newer and better models.
Does that sounds like a more reasonable way to go? Our budget for a single camera for one of the kids has always been no more than $100 and well, buying brand new, you just can't get much for that amount. Believe me, if we could afford to buy them all a nice, top of the line P&S, we would. But again, there are six children. Not going to happen.
Can you think of any specific brands that are now 3-5 years old but were/are great cameras, so that I have something specific to look for?
Or maybe a suggestion as to another solution for the kids?
TIA