Heat grill to high. Whisk together coconut milk, curry paste, onion, cilantro, lime juice, and oil in a large bowl. Season, to taste, with salt and pepper. Place shrimp in the bowl and toss to coat. Cover and let marinate at room temperature for 20 minutes.
Remove shrimp from the marinade and grill for 1 1/2 to 2 minutes per side. Serve on brown paper bags, if desired.