Both my son (10 years old) and daughter (8 years old) enjoy making doll sized quilts for wallhangings. The key with the quilting was to set the speed on my machine to the lowest setting, so they could get used to feeding it through.
When my son was 9, he made a throw sized quilt with large panels and simple sashing. We did the pillowcase method of flipping the quilt inside out, adding batting and then tying the quilt.
The main thing I emphasized to them was to take their time and to make sure that the seams lined up correctly. One of the first projects I started them each on was a four or nine-patch block.
You could also make simple bags or pillowcases like GagaSmith mentioned.