So, I am trans and also had a super christian family (my dad was a pastor). It took years before we were able to get to a place where my parents and I talked again, and more to get into a place where they were accepting, even if not approving. So, while I can't know your specific situation, I think get it. It sucks. I was probably somewhere around your state of mind when I tried to OD. Not only did it not kill me, but it hurt the entire time. The 28 hours in the ICU were the most miserable of my life, and I did a tour in Fallujah as US Marine. Ironically, it was after that, when I was in the psychward after that my dad flew 700 miles to see me to see if I was okay that started the healing process.
Even a successful overdose will likely result in a painful, miserable death. Keep in mind the LD50 is only sufficient for killing half the test sample. If you only take the LD50—which for most of the over the counter pills, or easily obtained pills—is a lot of pills.
So, to answer your actual question, the way to successfully overdose, on anything, is to get a giant bottle of pills, way more than you think you will need. Then sit down with a bit of water and swallow them all.