Here are some great websites that I stumbled upon.
1. Learn each of the keys from Dance Mat Typing
This is a full-fledged typing course for kids, systematically teaching them practically every key of the keyboard. The lessons are animated and fun, and while I think some time is wasted in the animated sections of the lessons, the step-by-step process is very thorough. The program is unintimidating and highly effective.
2. Practice typing full words and sentences with Keybr.com
Once all the keys on the keyboard are learned, children can move on to Keybr.com. They have the choice to practice typing random words/non-words, to practice custom text, or to practice the text from any website or blog. Practicing typing real words is the best way to hone a child's typing skills, so I'd suggest using the custom text of website/blog option. (You'll need to click the button above the keyboard next to word Tutorial to change the text settings.)
Keybr.com shows the student's speed, errors, as well as the particular keys which are the weakest. This site is extremely well-designed and offers enough custom features to make it useful for a long time without getting boring.