For me (a nail-biter by heredity, I think), the best solution is to get up and move, do housework, play, go for a walk. I believe most nail-biting kids have a lot of pent-up energy and unconscious tension that they must control to "fit in" to whatever is going on around them. Even if they look relaxed, their bodies could be begging for movement. In fact, they could look relaxed BECAUSE they are using a coping behavior.
I started biting my nails early, and tried to stop for many years. I even bought my own stop-biting liquid, and tried every technique I could think of, including giving myself manicures as I got older. I finally – mostly – broke the habit in high school, but it was not because I used any tricks, but because I really, really wanted to quit. For myself, not for my mom or my teachers. And I began working on the anxiety and tension that prompted this coping response.
I hope you will work to reduce your own anxiety and negativity about this, because intensity from you could inadvertently increase your child's stress. I think my habit was aggravated by an over-involved and very controlling mother. In my experience, embarrassment, shame, scolding and nagging not only do not help, they probably increase my need to nibble and tear. And fingernails are handy! Require your daughter to keep her hands clean if she's going to put them in her mouth, and maybe help her find something else satisfying to bite, or fiddle with with her hands. Help make physical activity possible as often as you can.
If you can somehow "force" her to quit, which I doubt you can, she is likely to substitute some other habit that will help her deal with the underlying causes.
By the way, other moms have asked similar questions and got quite a few interesting responses. You might want to check these out: http://www.mamasource.com/request/8031309387765121025 and http://www.mamasource.com/request/recent/97013/1202607294/85