Place the chicken thighs in the slow cooker and sprinkle the jerk seasoning evenly over them. Pour the chicken broth around the chicken to keep it moist during cooking.
Cover and cook on low for 6 hours until the chicken is very tender and easy to shred with a fork.
While the chicken cooks, combine the diced mango, red bell pepper, cilantro, and lime juice in a bowl. Stir gently and add a pinch of salt if needed. Set the salsa aside in the refrigerator.
When the chicken is done, remove it from the slow cooker and shred it with two forks. Return the shredded chicken to the slow cooker and stir it into the remaining juices.
Warm the black beans in a small pot or in the microwave. Serve the chicken topped with the mango salsa and a scoop of black beans on the side.