There is one village in Nigeria where the men and women speak different languages. Not sure if that is a satisfactory answer.

Puerto Rican Spanish, the men speak a more ‘street’ less formal dialect, while women speak a more formal dialect. Heavily influenced by music.

One of the many debated claims about Pirahã is that female speakers can’t use the phoneme /h/, always substituting /s/ instead.

California. In the 90s, women started up-talking, that fucking annoying habit of saying everything as if it were a question.

There are a bunch of cultures where a ‘sacred language’ is permitted only for men, or there are distinct languages used by only men and only women. Unfortunately, my memory isn’t so good as to remember what those languages are. A quick search shows that the Kallawaya language is a ‘secret language’ passed down usually from father to son, and to daughters only if a man has no sons.

Check out ‘Gender role in language’ and the topic of genderlects; Gender differences in Japanese; Nüshu script.

You could also try looking through above-mentioned sacred languages and ritual languages for whether it’s mentioned that any of them are specific to a gender.

Kashyyk probably