Combine first 4 ingredients in a small bowl, stirring well with a whisk. Brush 2 tablespoons vinegar mixture on fish; brush remaining vinegar mixture on onion slices. Let stand 10 minutes.
Place onion slices and fish, skin sides down, on grill rack coated with cooking spray. Grill onion 4 minutes on each side or until lightly browned and tender. Grill fish 4 to 6 minutes on each side or until fish flakes easily when tested with a fork.
Coarsely chop grilled onion, and place in a large bowl; add cheese, olives, and capers, tossing well. Serve relish with fish.