If having sex without a condom is stupid, why are you listening to her? Unless she’s willing to be tested for STDs and go on the pill, stop this dangerous and stupid behavior.

To answer the second part of your question, the answer is yes, but to get to that yes is not that easy. A woman can only get pregnant for a few days a month, but figuring out when it is safe and when it’s not is difficult if you want to know with 100% certainty. Some women have regular periods and you could guess when she is fertile (about two weeks after her last period), but even women who are regular sometimes go off schedule, so you could guess wrong. Some women can sense when they’re ovulating, it’s a pain called mittleschmertz. If you’re having sex with a woman who knows when she’s ovulated, then that would certainly help you figure out which times of the month were safe. But again, just because she’s ovulated and shouldn’t ovulate for another month is no guarantee that she’ll ovulate next month at the exact same time, so you’d have to abstain from sex for at least a week, and even then not be 100% safe. Now there are other means of telling when a woman is going to ovulate which include taking her temperature as soon as she wakes up and checking the stickiness of her cervical fluids. Altogether these methods are called Natural Family Planning, and they’re important to people who want to have a baby and can’t, as sometimes they can be helpful. But to use these methods to prevent pregnancy is so complicated that most people don’t even try. And of course, NFP won’t protect you against STDs. So rather than continue listening to this woman, start using condoms.