Heat oil in large saucepan over medium heat. Add pineapple, onion, paprika and salt. Cook 3 to 4 min., until pineapple and onion are starting to soften and paprika is fragrant.
Stir in vinegar and barbecue sauce. Reduce heat to low and simmer, stirring often, 10 to 15 min., until sauce has thickened and reduced. Remove from heat and stir in cilantro.
Substitute red wine vinegar for cider vinegar.