May one play tennis with wife when she is a niddah?
There is no formal prohibition involved in a game of tennis, but doing so is not proper practice, and must be avoided.
The Terumas Hadeshen (251), which is cited by the Rema (195:5), prohibits (or writes that this not clear to permit) going on a carriage with one’s wife for the purpose of going on an excursion. The idea is that going on a joint excursion can lead to intimacy between the couple, and such situations should be avoided. See, however, Iggros Moshe, Yoreh De’ah 1:92 and 2:83.
With regard to playing chess and ping pong, the Be’er Moshe (50) writes that under extenuating circumstances one can be lenient. Divrei Shalom (84), however, though finding no formal prohibition, writes that one cannot be lenient under any circumstances in such matters, writing that it is known that such games are liable to lead to intimacy.
Therefore, although there is no formal prohibition, a game of tennis brings the couple towards intimacy, and must therefore be avoided.