Indeed, it is an answer form when asked: John, do you play tennis?
John answered: I do play tennis or -Yes, I do play tennis.
So, I do play tennis is absolutely correct & formal.
Following samples are same with do before a verb:
Do you smoke? Ans: Yes, I do smoke
Do you eat a lot for dinner? Ans: Yes, I do eat........
yes u could use like this, but only in informal english, like i DO love somebody....i DO like somethings, it used to emphasize the "verb", in your case, i DO play tennis, means u can play tennis very well.......