Hello Woody30, a couple of questions.. what other buildings, lines of tall trees, hills or valleys are near your house?? If you are in a low area, with tall trees around, or have several two-story houses nearby, then you will in effect be in a valley, and may have issues with a minumum size chimney.
If your home is on high ground, without any blocking buidings or tree lines, then a chimney as described by Hitzer should work fine for you.
As posted above, having more chimney than needed is better than less. But you do have the option of building to the Hitzer-described minimum, then if you feel you need more chimney, you can bring back your mason, and add several more courses of chimney block to raise the height.
Another variable that has not been mentioned yet are weather variables.. Are you planning on starting to burn coal early, like November and burning late, like April?? When the outside temps rise, the draw from a chimney decreases, so this can change the design requirements of your chimney.
Yet another variable is your home, is it a tight, modern home with well sealed windows and doors?? If so, then your chimney will have a harder time drawing air through your coal stove.
I believe that if you provide an outside source of air to the inlet of your stoker motor, or to the air inlet area of your stove, you will be able to function well with a chimney that is 18-20 above the thimble. Without an outside air source, the chimney must be strong-drafting enough to overcome bathroom vent fans, cooking stove vent fans, clothes dryer venting. If all the mentioned appliances are running at the same time, then there is a significant draw on the house, and a chimney must have more draft than this to keep from reversing flow. With it's own outside air source, then this scenario isn't a problem.
My recommendation, without knowing the placement of your home would be to go with an outside air source and a 24' chimney, this would be 6' above your peak, a foot or so less may be fine if you don't have any tall trees, hills or buildings blocking your home. This would provide roughly 18' above your thimble, and with it's own outside air source, the coal burner and chimney should function fine.
Hope this helps. Greg L