Try a product called "Thum" sold at most Walgreen's in the baby section. It's mildly hot and supposed to taste nasty to the child.
I used it with my son and it did work at first. However, with time, he just decided to eat the nasty stuff anyway.
I then resorted to using non-acetone nail polish remover...the kind where you dip your finger in the jar which has a sponge with finger holes in it. Any brand will do (we used Walgreen's generic remover), and all put something called "Bitex" in the solution to make it bitter tasting so kids will be naturally discouraged. It's incredibly nasty. It definitely will discourage nail biting.
However, keep in mind, nail polish remover is not safe to ingest. So use sparingly and when not using it, keep it out of your child's reach.
For us, the Bitex is so bitter tasting (I tried it myself), after one session of dipping my son's finger tips/nails in the solution and letting it dry on them.. he took one taste and that was the end of that. He hated it. I only used it a couple of times to get the point across. He doesn't bite his nails anymore.
Since this isn't the intended use of the product, and it is a chemical, maybe use a q-tip and swab a little on his nails rather than dipping his fingers. Most important Keep it out of reach of your child, though it's so nasty he'll more than likely avoid it anyway.