The best answer is time. My cousin (white) has been married to her black husband for years and they have two adorable twin boys.
However, when they were dating her parents would not accept him in their lives. It took years before they realized he wasn't going anywhere and they finally accepted their daughter was happy. With the blessing of both families, the couple eventually wed. They realized, that black, white, or green, how great this man really is.
Now, years later, her sister has married a terrific black man as well. Fortunately for her, my aunt and uncle welcomed him into their lives with little or no reservations.
While it may take time, if she is dedicated to her relationship and the man is truly the one for her, they may finally accept him into their lives.