There really aren't many (if any) words that can "replace" play as it's used in your examples.
Its conceivable that you could say "I participate in a game of tennis each day" but that sounds stilted and does not replace the word "play" as you wish. Some could argue that "participating" is not the same as playing. After all, the referee participates in the game too.
As for basketball, you could say "I shoot hoops with my friend on Sunday", but this is highly colloquial and I have also replaced the word "basketball." You could also say "I take on my friend in a basketball game on Sundays", but this also changes the order of the sentence and does not strictly replace the word "play."
Please note that the answer "I take the tennis every day", is incorrect. It's not a sentence and it doesn't really mean anything.
Sorry I cant find a synonym for you but I'm afraid this is one of those cases where only one word really fits. Maybe my colleagues have other suggestions?