Gluten-free replacement for all-purpose flour in fried fish batter?
In general, if something is burning too quickly, you need to turn down the heat, and cook it for longer.
As for recommendations for gluten free batters, there are plenty of gluten free tempura batter recipes out there that use rice flour.  Although it's worth noting that tempura is usually only cooked to 'golden' in color, not fully 'brown'.
And if you're willing to go with a three part breading instead of a batter, you can use rice flour, egg, and (rice or corn) cereal crumbs.