Pat both sides of slabs dry with paper towels. Using a sharp knife, remove thin membrane from back of each slab by slicing into it and pulling it off with a paper towel. (It can be difficult to remove the membrane from beef ribs, so you might want to have the butcher do it for you.)
Combine salt, coffee, pepper, paprika, and chili powder in a bowl; rub evenly over both sides of each rack, and let stand at room temperature 30 minutes.
Prepare a charcoal fire in smoker according to manufacturer's instructions, bringing internal temperature to 250°F to 275°F. Maintain temperature for 15 to 20 minutes. Place wood chunks on coals.
Place ribs, meaty side up, on smoker; cover with lid. Smoke ribs, maintaining inside temperature between 250°F and 275°F, until meat begins to pull away from bones but is not yet tender, about 3 hours. Brush about 1/2 cup Cola-Coffee Barbecue Sauce over both sides of ribs. Cover and smoke until a meat thermometer inserted in between the rib bones registers 205°F and rib meat is very tender, about 1 hour and 30 minutes, brushing with about 1/4 cup barbecue sauce every 30 minutes. Remove ribs from the smoker; brush with 1/4 cup barbecue sauce. Serve with remaining barbecue sauce.