You're not likely to get much in the way of features, image quality or durability at that price, but I do think I've seen a few off brand models on a rack at Target for under $75. Looking for something used on eBay or Craigslist might be a better option. There are some cameras intended for children at that price, but at least some of those don't have a rear lcd, and in my experience kids don't think it's a camera unless they can see the picture immediately after taking it.
Edited to add: I just did a quick search on eBay for a digital point and shoot camera with 3-4 megapixels (because it's probably plenty of resolution for a kid's first camera and I figured there would be some deals) in the completed listings and found quite a few Canon, Kodak and Fujifilm cameras in good working order that sold for around $50.
Also, I just remembered that a friend of mine bought her kids some little combo video/still cameras at Best Buy last Christmas for around $70 each. They love them. My 8 yo dd has a Nikon p&s that we bought for her 7th bday and she uses it more for video than still pictures.
Hi,
I just bought an hp E337 at Meijers this week for $49.99. I bought it because of its size and the fact that it takes AA batteries. I wanted something to keep in my purse all of the time. It got great reviews on Walmart.com http://www.walmart.com/catalog/product.do?product_id=7811061 . Most people were buying it for children. It does not have the quality as our other cameras. We have a Canon S5IS, Nikon D70s, Canons A95 and A70, but we started with a little HP that took decent pictures, so I thought for $50 I could not go wrong in trying this out.
It is about the size of a deck of cards, has a fixed lens, and takes 2 AA batteries. I can carry it with me all the time and not have to worry if the battery runs out, I can pop in anywhere and grab a couple of AA's. This won't replace any of our other cameras, but I will have a camera if I ever need it, and if it gets lost or stolen, I am not really out that much.
I have taken a couple of practice pictures and it appears to do great outdoors and acceptable inside. I hope this helps.
The more I think about it, the more I think I'd go the used route. If your 7yo is anything like mine, s/he'll love to "play" with the various features on the camera--scene modes (which aren't a bad way for them to learn about aperture, shutter speed, etc.), zoom, video mode, and so on. If you go with a bare bones model, you're not going to get much of that.