Stir scallions, garlic, ginger, chile, soy sauce, 1 tablespoon lime juice, allspice, thyme, cinnamon, salt and broth in a 4-quart slow cooker. Add thighs and turn to coat.
Cover and cook on low for 5 hours. Add green beans around the chicken and cook covered on low for about 1 hour more until beans are tender and chicken reaches at least 165°F.
During the final hour, bring rice and 1 1/2 cups water to a boil in a covered saucepan, reduce to low and cook for 40 to 45 minutes, then rest covered for 10 minutes.
Toss pineapple with the remaining tablespoon lime juice in a small bowl.
Lift chicken and beans from the cooker and spoon a little cooking liquid over the meat.
Divide rice, chicken, beans and fresh pineapple among 4 plates.