I have never convinced anyone to try them, exactly... but I have done stuff adjacent to getting them to try psychedelics. My little brother was curious, and on the fence about their safety and worthiness as something desirable to do, and I convinced him they had something valuable to offer. But he never actually did any, it was always a "maybe sometime we can take mushrooms together", but it never materialized, and now he has 2 kids and has taken the possibility off the table. I still talk to him about my experiences, though.
I convinced my mom that psychedelics were not just some scary drug that rebellious teens do, too. Many years ago, but years after my early psychedelic period that changed my life, I got into a long conversation with my mom, which eventually went to her being sad for me and my siblings, who moved away from Christianity as we became adults. She said it's not that she wants us to believe ant specific thing, just that she feels it's important to believe in something greater than yourself. I had opened up a bit to my mom about weed by then and she grudgingly accepted it, though it was a bit colored by my getting caught and scaring them in high school. So I took a shot and told her about my first trip with mushrooms, and how it changed my life, and what happened, and what it was like. She was super interested and curious and told me she was happy for me, and said that she had no idea that psychedelics could actually be a positive thing but that considering the positive change they facilitated for me, she was grateful that they existed and happy I took them.