Rinse scallops and blot dry on paper towels.
Heat a large nonstick skillet coated with cooking spray over medium heat. Add scallops; sprinkle lightly with 1/4 teaspoon salt and paprika. Cook 3 minutes on each side or until opaque in center. Remove scallops with a slotted spoon. Set aside; keep warm.
Add coconut milk and ginger to pan drippings. Cook 1 minute, scraping pan to loosen browned bits. Remove from heat. Stir in butter and 1/4 teaspoon salt; stir until butter melts. Pour sauce over scallops. Sprinkle with black pepper.