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There is also a website called Hellosensei where you can find personal tutors for your child.
Your response just reminded me - my neighbor tutored elementary school students online.
Another place to try is italki. Some teachers offer English lessons for children.
Hello Sensei.com has teachers who live in Japan and most people meet in person for their lessons, I did it for a short time. Of course if you want to have just an online teacher, that is possible too.
Try kouminkan in your neighborhood. There may be children's English lessons there. Also have a look at the noticeboard as English teachers and eikaiwas may have posters.
Try searching with Google and check out the reviews of local eikaiwa. Ask the eikaiwa if you can do kengaku. See if their programs and teachers are a good fit for your children.
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