"I don't play tennis on a rainy day."
I'd confuse は in this sentence with に for "on" as a preposition, since the subject is "I".
Somedays Japanese nuances really never fully click....
It's impossible to translate things word for word. The functional parts of Japanese are just fundamentally different from English, so you always have lots of reading between the lines to do.
Are you trying to talk about rainy days, or are you trying to talk about yourself?
雨の日は... is sort of like "As for rainy days..." - you're setting the stage for talking about rainy days.
雨の日に... doesn't change the topic of discussion which we might assume is yourself.
You can also use them together:
雨の日には... is sort of like "As for on rainy days..." which is a little weird in English, but a natural way in Japanese to perhaps create some emphasis on rainy days there.