Bird Keepers existed in the Kanto, Jonto, Hoenn, and Sinnoh games, including the remakes. They specialize in Pokemon that are based on birds. I feel that they should be included in Pixelmon since we don't have any Trainer Classes that particularly favor Flying-type Pokemon (though not all the Bird Pokemon I suggested below are Flying-type, for example, Sirfetch'd, Decidueye, and Espathra aren't), and there are so many Pokemon that fit the class. If a Flying gym gets added, Bird Keepers could be the dominant Trainer class for the Gym Trainers.
- Bird Keeper Pokemon Pool | Show
If you are daring, you could even put MissingNo in the pool of Pokemon, since it was Bird-type in the main games. Of course, MissingNo is not meant to be used as anything but an error handler in Pixelmon, so you don't have to.
As for biomes, I think the All Forests category would be a good fit, so that this Trainer class spawns in Forests, Birch Forests, Flower Forests, Taigas, Dark Forests, Giant Tree Taigas, Giant Spruce Taigas, Ultra Forests, and the variants. Birds often live and nest in trees, but aren't usually a fan of the cold (many birds migrate before winter), so this is the best category for the Bird Keeper to spawn in.
Edit: I decided to put strikethroughs through all the Pokemon in the non-legendary list that SKyTheThunder suggested removing from it, as I do agree with the suggestions and was thinking the same thing myself. Still plenty of options.