In a small bowl, combine the cranberries with the brown sugar and vinegar. Let sit for about 10 minutes.
Season the drumsticks with salt and pepper. Combine the rosemary, garlic powder, and paprika. Sprinkle all over the chicken. Heat about 2 tablespoons olive oil in a large skillet. Brown the chicken in batches.
Place onion in a 9 by 13 baking dish. Place the chicken on top of the onions, add the cranberry mixture and chicken broth. Bake for 35-40 minutes or until the chicken registers 165 degrees on an instant-read thermometer.