A cooking device may be for a solid-fuel cooker that includes a firebox, a cooking plate carried adjacent an open upper end of the firebox and defining a cooking surface, and a lid to be carried by a sidewall of the firebox over the cooking surface. The cooking device may include a fuel container for carrying the solid-fuel therein and to be carried within the firebox spaced inwardly from the sidewall. The fuel container may include a tubular lower body having opposing open ends and a lower body sidewall having a plurality of air openings therein, and a tapered upper body having a larger open end open toward and spaced below the cooking surface and a smaller open end coupled to an open end of the tubular lower body. A solid cover may be carried by the larger open end of the tapered upper body.