Kenny and Byron both start out as kids. (Duh alert!) Byron is a foolish teenage delinquent, and Kenny is an innocent, dinosaur-wielding ten-year-old. By the end of the book, the boys haven't aged significantly, but they have grown up. They've both learned a few tough lessons and seen the darker side of the world. They've had to accept some really heavy stuff like death and violence and racism, and they've had to realize that life goes on in spite of these awful things.
All that makes Watsons a coming-of-age story. It's not about reaching a magical birthday when the character is suddenly an adult; nope, it's about learning stuff that brings the character a little farther into the grown-up world. And that's just what happens to Kenny and Byron.
Watsons is pretty obviously also a family drama. From the book's title to the end, this story focuses on one thing: the Weird Watsons. The most important relationships in the book are those of this family, the major conflicts are family conflicts, and the solutions are found in the family, too.
Last but not least, we've got historical fiction. Watsons tells a fictional story (about the Watsons) taking place during a specific historical event (the real bombing of the Sixteenth Street Baptist Church in Birmingham, Alabama, 1963). The author preserves the major historical details of this event (the bomb was put in the church by white men, it went off during Sunday school, four girls died), but adds the Watsons in as bystanders.
Their presence doesn't change the historical facts, but by putting characters we know and love right into history, we are able to understand this tragedy in a new way; we get a completely different perspective than if we had read about it in a textbook. Historical fiction is all about opening up history through the eyes of fictional characters—and there's no questions Watsons does just that.