Place sliced onion and garlic at the bottom of the slow cooker.
Rub pork with paprika, salt, pepper, and chili powder, then set it on top of the onions.
Pour barbecue sauce and Dr Pepper over the pork.
Cover and cook on LOW for 8 to 10 hours, or until the meat shreds easily with a fork.
Remove the pork, shred it with two forks, then return it to the slow cooker and stir into the juices.
Serve warm on sandwich buns with extra barbecue sauce if desired.