Question

my sister doesn't or don't play tennis​

Answer 1

Answer:

my sister doesn't play tennis

Explanation:

The Only One rule of the "subject-verb-agreement" says it that singular subjects go with singular verbs and plural subjects go with plural verbs

Answer 2

My sister doesn’t play tennis.
“Doesn’t is a contraction of does not.
“Don’t” is a contraction of do not.
In this case, “doesn’t” would be correct because your sister not playing tennis is consistent. She doesn’t play tennis now and likely will not for a while, if she ever does.