I am a kindergarten teacher at an international school in Osaka (actually, I'm on hiatus at the moment, but whatever). This is what I've noticed over the years as a teacher:
Immersion is critical. The difference between the kids who live their lives in both languages and those who study it intermittently is quite noticeable. If you can afford, and are close enough to, an international kindergarten, do it.
Create language environments. What I mean by this is: home is always English, school/outside/grandparents' house is Japanese; dad always speaks English, mom always speaks Japanese, etc. This will teach your kids to separate the languages naturally. In my classes, and in front of my students, I never spoke Japanese, even if the kids did. This forced them to attempt to communicate with me in English. I would remind them if necessary.
Read to your children, from the day they are born. Lay them on your chest so their ear is near your voice box, and read children's' stories to them. This helps establish the sound recognition of the language. (A friend of mine did this, and he said it was very effective.)
Sing songs. Again, this is for sound/rhythm recognition purposes.
Know that the kids will mix the languages as they attempt to communicate. Eventually, they will learn to separate them.
Remember that the kids will learn at their own pace. In my last class last year, the youngest student was one of the brightest and most proficient at both languages.
Check out the book ''How to Multiply Your Baby's Intelligence.'' We used many of those techniques with the pre-school kids (pre-school being 1-2 years old) and even the first-year kindergarten kids (3 years old--this was the level I taught).
If you are in Tokyo, there are tons of international schools around. If you are in Kansai, there are some, but not as many. Elsewhere in Japan, I don't know.
If you have any questions, especially regarding the Kansai area, feel free to PM me.
Hope this helps.