My older brother went out with a hardcore Christian for a year and a half. They were really really close but could never have sex. He never tried to convince her simply because he's a good guy and knows she's a bible basher. In the end, their indifferences (her religious hogwash and his free spirit) clashed too many times and they went through a very painful breakup (although mostly for my bro).

At the risk of sounding pessimistic or cynical, if this girl is bent on holding on to those beliefs then I believe it's a lost cause. A narrow minded partner will only cause you grief in the long run. If however she assures you she's willing to be turned then I would just be patient and give it time. It sounds like your pretty close and if that's the case, these things unfold naturally. Give her a lot of space when your getting physical and don't try to charge in there like a horny bastard. You've gotta give her time to get over her hangups and as long as it takes, it'll be worth it in the long run.

I wouldn't recommend taking any drugs beforehand (particularly weed). That's definitely the wrong way to go about this.

EDIT: Also, if it's any help. I was pretty hung up about sex when I got with my girlfriend two years ago. I was nervous and hesitant simply because I didn't know very much about it and didn't feel those emotions. She waited patiently for me for 6 months before we took it one step at a time. Now, without going into too much detail, it's aaalll good. It's just time man.