Special equipment: a 6-quart slow-cooker
Coat the insert of a 6-quart slow cooker with cooking spray and place 3 to 4 canning jar lid bands (without the flat metal rounds) in the bottom. Combine the paprika, garlic powder, pepper, salt, coriander and cumin in a small bowl.
Dry the chicken well and turn it upside down. Cut a 1-inch-long slit in the skin between the thigh and the backbone on each side. Rub the spice mixture all over the chicken, making sure both sides are evenly coated, and place the chicken in the slow cooker on top of the lid bands. Cover and cook on low until the chicken is tender and cooked through, about 7 hours.
Meanwhile, make the barbecue sauce: Combine the ketchup, vinegar, brown sugar, mustard, salt, chili powder, onion powder, garlic powder, cayenne and pepper in a medium microwave-safe bowl and microwave for 4 minutes, stirring once halfway through, until the sugar and spices are dissolved and the sauce is thickened. Let cool completely.
When the chicken is ready, remove the lid from the slow cooker and brush the chicken with barbecue sauce to cover well and let it rest for 10 minutes. Carefully lift the chicken from the slow cooker by putting tongs into the cavity, and sliding a spatula underneath and transfer it to a platter. Serve additional barbecue sauce on the side.
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