Prepare the Pork: Mix paprika, garlic powder, onion powder, brown sugar, salt, and pepper. Rub the mixture all over the pork shoulder.
Slow Cook the Pork: Place the pork in a slow cooker and pour cola over it. Cook on low for 8-10 hours or on high for 5-6 hours, until tender.
Make the Cola BBQ Sauce: In a saucepan, combine BBQ sauce, cola, brown sugar, and apple cider vinegar. Simmer for 10-15 minutes until thickened.
Shred and Sauce the Pork: Shred the pork with two forks, discard excess liquid, and mix in the BBQ sauce.
Assemble the Sliders: Pile the pulled pork onto slider buns and add toppings if desired. Serve immediately.