Combine first 4 ingredients (brewed coffee through molasses) in a large ziploc plastic bag; add pork. Seal and marinate in refrigerator 2 to 12 hours; turning bag occasionally. Remove pork from bag; discard marinade.
Prepare grill; heating one side to medium and one side to high heat.
Combine ground coffee and next 4 ingredients (sugar through sea salt); rub over pork. Let stand at room temperature for 15 minutes.
Combine 1/4 cup barbecue sauce and 1 tbsp. apple cider vinegar. Reserve 2 tbsp. of the barbecue sauce mixture; set aside.
Place pork on grill rack coated with cooking spray over high heat; grill 3 minutes, turning pork on all sides. Then place pork over medium heat; grill 15 minutes, turning pork occasionally. Baste with the 3 tbsp. barbecue sauce mixture; grill 5 minutes or until temperature registers 160 degrees F (slightly pink), turning pork occasionally.
Place pork on a platter; brush with reserved 2 tbsp. barbecue sauce mixture. Cover with foil and let stand 5 minutes.