I don't know how much it will help but I grew up very very close to my grandmother. She practically raised me. My family has never been one to be overly religious, so I'm not sure how to handle that sort of situation, but a part of my family is rather religious. But if they were accepting, for the most part, of their son being gay, then I can believe they're pretty open minded individuals that will not understand, so it will take time to explain and deal with, but they seem to me to be open enough to at least try to understand you rather then dismiss you.
I came out to my grandmother in a letter. I am a horrible speaker, I get nervous and start stuttering. I knew that I could never get the words out vocally. So I wrote a letter to her, and gave it to her, in tears at the time, telling her it was really important and would explain a lot of things, including my suicidal history in which she was the first take notice due to the same signs of previous suicidal family members. She didn't understand. But she knew I meant the words, she knew I needed help. And since she's done everything she's can to help me, including helping me tell others in my family. All of which are surprisingly accepting, even the religious ones.