To be able to reserve public tennis courts in Tokyo, you will need the Tokyo Sports Facilities User Card (東京都スポーツ施設利用者カード), issued by the Tokyo local government. You can apply for this card at any of the Tokyo public parts that have tennis courts, including Hibiya Park, Shiba Park, and Kiba Park, and Ariake Tennis Forrest Park.
Applying is very easy and shouldn’t take more than 10 minutes for you to get your card.
After you get your card, you should be able to login at the Tokyo Sports Facilities Service Website (東京都スポーツ施設サービス). This will allow you to reserve courts if there are openings, or join the monthly lottery.
For the more popular locations like Hibiya Park and Shiba Park, you’re only chance is to win the lottery. For the less popular ones like Toneri Park, you can just wait for people to cancel their reservations and apply for the slot.
Remember that people are allowed to cancel only until 4 days before the reserve date so if you plan to wait for people to cancel their Saturday reservations, people usually cancel their reservations on Tuesday night.
From experience, it’s also possible to call the courts directly and ask if there are openings. Just be ready with your card number as they would ask for it.