It would all depend of the level of technology your world has and how wedded you are to the idea of lifting a wooden ship complete with a hole in the side and useless bowsprit along with all the other heavy junk a sea ship needs to weigh it down so winds don't make it capsize. If so I'd consider making it out of Martian liftwood (Space 1889) with a varnish of <PERSON> Cavorite (First Men In The Moon). Weight vs Buoyancy is the primary issue. However lets assume that your civilization has advanced material science but just never got around to developing internal combustion engines (piston or jet) or lightweight electric motors and fuel cells. The reasons I'll leave up to you. In that case it is definitely possible. Consider the Magesterium airship seen in the movie The Golden Compass. Discard the fantasy 'anbaric' thrusters and the oversized tail fin and you have a basic dirigible/blimp with one important addition. The gas bag filled with lift gas (helium or hydrogen) has a secondary chamber surrounding the front end. See the picture. I would suggest that a secondary liftgas fills this chamber. One that can be adjusted in buoyancy, isn't flammable, and doesn't need the heavy complication of high pressure cylinders and compressors. 308
That liftgas would be steam. Steam has over twice the lifting power of hot air and you will have plenty of it in the engine exhaust. Modern day polyester mylar, teflon and a new recent flexible aerogel would make a lightweight and durable laminate balloon material with good thermal retention properties. As steam condensed it would drain down to a reservoir for return to the boiler. This will eliminate the need for a separate condenser further lightening your airship. Since you are insisting on coal as a fuel I would suggest a fluidized bed combuster with bed of a lightweight refractory sand, possibly alumina. Over it would be a flash boiler similar to that used in the 1910 White Steam Car. The steam engine would be a smaller simpler version of the radial steam turbine used in the 1894 Turbinia steamship. Of course everything would be constructed of lightweight polymers, and aluminum and magnesium alloys. Heavier metals would be used only where absolutely necessary and kept to a minimum. Aerogel would be used for insulation where possible. If you designed it properly I think you could get a pretty respectable performance out of a vehicle like that. 479