We went through this at my house, too, and I wish I had some miracle fix, but, alas, I don't. My daughter spent several years as a nailbiter. Here are a few things that at least seemed to make it less frequent a problem.
There's a Berenstain Bears book called The Bad Habit that helped her to understand what bad habits are and to make her aware of possible triggers. She chewed her nails when she was concentrating deeply on other things, such as at storytime or when she was watching TV. Once she understood that, I was able to say to her, "Your fingers are in your mouth," and she did get that I wasn't nagging, just making her aware of something she hadn't noticed she was doing. It also happened mainly during the school year. Her first grade teacher (a very special, compassionate lady)noticed that she did it a lot during math, the only subject she is anxious about, so she (with my permission) allowed her to discreetly chew gum during math time at school. This did help a great deal. It cut way down on the problem, although it did not eliminate it entirely. But what finally got her to kick the habit (other than time, patience, and a little maturity) was a huge bribe - I told her that if she could go 2 weeks without any nailbiting at all, I'd pay for her to have a big girl manicure. Which is why this last week (finally!) my daughter had teal and hot pink nails with white butterflies on them!