In a large bowl, stir together 2 cups water, coffee, salt and sugar until salt and sugar are completely dissolved. Stir in chili powder, red pepper, garlic and cinnamon. Add chicken. Top with a small plate, if needed, to keep chicken submerged. Cover and refrigerate for 2 to 4 hours.
Preheat broiler. Lift chicken from brine and place on a broiler pan. (Discard brine.) Broil 4 to 6 inches from heat source until browned, about 10 minutes. Turn chicken pieces and broil until second side is browned, 10 minutes more.
Set oven to 350°F. Move pan to a rack in middle of oven and bake until drumsticks are no longer pink at bone (cut to test), 10 to 15 minutes longer. Serve hot.