You can get the single-use camera from Kodak, it meets all of these criteria.
A camera for a child aged 4 to 10 should be
-hard to break
-cheap to replace
-simple to use
-with a low per-exposure cost
If you think the kid is ready for a "real camera", a simple point and shoot is probably a reasonable purchase:
- Olympus Infinity Zoom 80 QD (film)
- Kodak C653