I don't know that there's any secret to coming out to conservatives. If they people can see past their point of view and love you for you, things will go well. If not, they probably won't.
My parents are quite conservative, but things went well when I came out. When things first came up, my parents weren't ready. Eventually they were convinced that being gay was just a phase, and I was tired of arguing.
Another year or so later the subject came up again, but this time we were able to have a conversation. Eventually my parents said that they don't care if I'm gay or straight, they just want me to be happy. They let me know that they love me.