1. Combine jelly, vinegar, grated ginger, and minced garlic in a small saucepan and simmer, stirring occasionally, until thickened and reduced by half, about 30 minutes. Remove pan from heat and stir in 1/2 cup chopped scallions; salt to taste. Divide mixture between 2 bowls, one for basting and the other to serve as sauce on the side.
2. Preheat grill. Bring 1-3/4 cups water to a boil with ginger slices and mashed garlic cloves. Add rice, stirring once, cover and cook on low heat 17 minutes (do not open lid). Remove pan from heat and let stand, covered, 5 minutes. Remove lid, discard ginger slices, add coconut and remaining 1/4 cup chopped scallions; fluff and stir rice with a fork. Salt and pepper to taste. Keep warm, covered, until ready to serve.
3. Rinse and pat chicken dry. Season with salt and pepper. Grill chicken on lightly oiled rack over moderate heat, turning until golden brown and almost cooked through, about 25 minutes. Brush chicken with basting mixture and continue to grill, turning once, brushing both sides with basting mixture, being careful not to burn (chicken will get black in spots), until cooked through, about 10 minutes more.
4. Serve chicken on a platter with rice, dipping sauce, and garnish with scallions. Makes 6 servings.