Combine 2 cups broth, beans, coconut milk, jalapeno pepper, thyme, and allspice in a heavy large saucepan. Bring to a boil over medium-high heat. Stir in rice. Reduce heat to medium-low and simmer uncovered until most of liquid is absorbed and rice is almost tender, stirring often, about 20 minutes.
Mix 3/4 cup green onions into rice. Continue to simmer until rice is very tender and mixture is creamy, adding more broth by 1/4 cupfuls if mixture seems dry and stirring often, about 5 minutes longer. Season to taste with salt and pepper. Transfer to serving bowl. Sprinkle with remaining 1/4 cup green onions.