If you're in the us, don't use a computer at all. Lot harder to get a warrant for a unlabeled calendar than it is to force you to unlock your phone, since there's a lot less bullshit you can make up (read: lie) about a calendar than someone's phone.
so i have no uterus so i can't seriously test it but there is
Mensinator https://github.com/EmmaTellblom/Mensinator
it's on fdroid and playstore, it's actively maintained and has 41 stars on github
it is private and local and it reads like you put it in the calender when you have your period and it gives you some statistics
drip, its on android (fdroid and gplay) and ios and actively maintained, local and private.
you can put in data like bleeding, temperature, cervical mucus, mood and some more. it seems to additionally give you reproductive information in the statistics
https://bloodyhealth.gitlab.io/
it's website suggests that it is financially supported by Mozilla which is cool.
again i can't really test these but after some clicking around, drip seems to have more features and better support
Also drip seems to be supported by the German ministry of education and science. Usually Germans rank privacy rather high in importance. So I think that speaks in favor of it too.