Hello cf1, Charlie Z, our 'offical greeter' has already welcomed you to the forum!!
As said above a good masonry chimney with a clay liner is just about the best chimney to have. The only exceptions would be if your coal burning appliance is one that needs lots of draft to work well and the chimney is too short, or too large inside dimension or situated on your house such that it doesn't draw well.
Sometimes a overly large chimney, with a small coal appliance that creates very little hot flue gas [exhaust] can't get enough volume of warm air to create a good draft. This would be about the only time a liner might be a good idea in an otherwise good chimney.
Tell us what type, brand and model coal burner you are planning on installing, what type of coal you plan on burning [bituminous or anthracite]. How big is the house, and how well insulated, how good are the windows etc. These pieces of information will help us help you.