In a food processor, combine yogurt, tomato paste, green onions, garlic, ginger, cumin, coriander, salt and cayenne pepper; purée until smooth.
Arrange chicken in a shallow dish; coat with yogurt mixture. Cover and refrigerate for 1 hour or up to 1 day ahead. Remove from refrigerator 30 minutes before cooking.
Place chicken skin-side down on greased grill over medium-high heat; cook for 15 minutes. Brush with marinade; turn and cook for 10 to 15 minutes longer or until golden and juices run clear (or place chicken on rack set on baking sheet; roast at 350°F, basting after 30 minutes with marinade, for 50 to 55 minutes or until juices run clear).
Serve garnished with chopped coriander or chopped parsley.