Dear MrHonest,
I can sympathize with your plight because I have several close friends/relatives who are not saved, and it breaks my heart every time I think of them. But I have reluctantly concluded that, unless God tells me directly, it is not up to me to convert them. God is not necessarily looking to us for results. What He asks of us is to stay the course; run the race to completion, as Paul put it, and not compromise our own principles to "fit in" with worldly people.
All you can do is set the example for your sister and pray for her, constantly. If you exhibit enough peace and contentment in your own life, the hope would be that she begins to see the benefits of walking closely with God and ends up wanting what you have. But you need to approach her with love and patience. It will do no good to enter into arguments which neither of you will win.
And remember, all you can do is present your case, in the most patient and loving manner you can. Ultimately, it will have to be God who converts your sister. So don't get discouraged when she ignores you or dismisses your attempts. We must always wait on God to do things according to His timing, not our own.
God be with you in your struggles.