Following the usual eyecare tips may help. Here are some tips that I've read about to help protect your child’s eyesight:
Having a balanced diet:
A well balanced diet with green and red leafy vegetables like carrots, spinach and beetroot, also yellow fruits like papayas and mangoes (high in carotene).
Take breaks:
Try to remind your child to take a break after 20 mins of staring at the computer/tv screen. Best to look at some greenery that are a distance away.
These are very basic but would be good for protecting your child's eyesight. It may be difficult to take such frequent breaks. I find sitting near the window a good way to facilitate that. By having the computer near the window, one simply need to look out every once in a while. Really helps with reducing fatigue in the eyes.