Heat the olive oil in a large skillet; season the chicken thighs with salt and pepper. Sprinkle 1/4 cup cilantro over the chicken thighs; brown the chicken in the frying pan, 3 to 5 minutes each side.
Arrange the chicken in the bottom of a slow cooker. Place the sweet potatoes, red bell pepper, and black beans on top of the chicken. Mix together the chicken broth, 1/4 cup cilantro leaves, salsa, cumin, allspice, and garlic together in a bowl; pour into the slow cooker. Set slow cooker to LOW and cook for 4 hours. Garnish with lime wedges to serve.