When my kids were little (4 or so) and began to express interest as I sewed, I started them on my old Bernina with no thread and a coloring book page. Their "challenge" was to let the needle poke holes along all the lines on the page. It works great for that eye/hand coordination they need in order to sew. Pretty soon they were sewing their own beanbags to play with.
There's no reason a kid can't sew on a regular sewing machine... just keep the machine simple.