Prepare the pork: Rub pork shoulder with paprika, garlic powder, onion powder, salt, pepper, and cayenne.
Slow cook: Place pork in slow cooker with chicken broth/apple juice. Cook on LOW 6–8 hours or HIGH 4–5 hours until fork-tender.
Shred pork: Remove pork and shred using two forks; mix with barbecue sauce.
Pickle onions: In a small saucepan, combine vinegar, water, sugar, and salt. Heat until sugar dissolves, then pour over sliced onions. Let sit at least 30 minutes.
Assemble sliders: Place pulled pork on buns, top with pickled onions and optional coleslaw.