Grind the coffee beans into a powder. If using grinders in a grocery store or coffee house, choose the “espresso grind”. Combine the coffee grounds, brown sugar, cayenne, salt, black pepper, garlic, and smoked paprika in a bowl.
Pat the mixed dry rub on all sides of the pork roast. It is okay if some falls. off. Place the pork roast in a slow cooker. Scoop up any of the rub that fell off and toss it in the slow cooker as well. Secure the lid, turn the heat on to low, and let cook for 8 hours.
After 8 hours, the pork should be tender and should shred easily with a fork. Carefully lift the roast out of the slow cooker and transfer to a serving platter. Enjoy!