A cooking device may be for a solid-fuel cooker that includes a firebox for carrying solid-fuel therein and having a base and at least one sidewall extending upwardly from the base, and a cooking plate to be carried adjacent the firebox and defining a cooking surface. The cooking device may include a tubular fuel container for carrying the solid-fuel therein, and to be carried within the firebox and spaced inwardly from the at least one sidewall. The tubular fuel container has upper and lower open ends adjacent the cooking surface and the base of the solid-fuel cooker, respectively. The cooking device may also include a solid cover carried by the upper open end of the tubular fuel container.