Many older homes have no liner in the masonry chimney; this chimney liner is designed to keep all of the dangerous flue gases inside to chimney and away from the living quarters. But when you home has no chimney liner, there is nothing stopping the exhaust from the coal stove from entering into the home.
If you already have a chimney and it has no chimney liner or the liner is not in safe condition, you need to replace the chimney liner. The easiest method is installing a stainless steel chimney liner. If you already have a coal stove, you know that the stove is sensitive to the draft and needs a very strong draft to operate properly.
A round stainless steel chimney liner will improve your draft. Draft works in a circle, or a spiral like a tornado. When you install a round chimney liner the round aids in the draft compared to a square terra cotta flue that cause turbulence. With a stainless steel chimnney liner you have a couple options.
Recommended coal stove liner
First of all no matter what type of stainless steel chimney liner you install it needs to have insulation. This keeps the smoke warm and makes it exit the chimney faster and gives you a stronger draft. Also with any solid burning appliance stainless steel chimney liners are only UL listed with insulation. Do not skip the insulation. There are also a few types of insulation you can choose depending on your circumstances.
The best you can have for your coal stove chimney liner is a rigid 316L chimney liner. This rigid pipe gives you 20% better draft than a liner with a corrugated inner wall. Also since the rigid chimney liner had a smooth inner wall it is almost impossible for the fly ash to collect on any surface. So a rigid chimney liner will give you the best draft and the chimney will stay cleaner.
The other option you have is a 2 ply chimney liner. This chimney liner is used when the chimney is not straight. It is flexible but like the rigid rigid liner it has a smooth inner wall. This gives you the same benefits of the rigid but it also goes around bends that you may have in your chimney.