Combine the scallions, bell pepper, olive oil, lime juice, garlic, thyme, allspice, ginger, brown sugar, chile pepper and 1 tablespoon salt in a food processor; pulse to make a thick sauce. Refrigerate 1/4 cup for serving.
Season the hens all over with salt and pepper; poke a few holes into the bone side. Rub 1 cup of the jerk sauce all over the hens in a large bowl or pan. Cover and refrigerate for 2 to 4 hours.
Preheat a grill to medium; prepare for direct and indirect grilling: On a charcoal grill, bank the coals on one side. For a gas grill, turn off one of the burners after preheating. Remove the hens from the marinade, letting any excess drip off; place skin-side up on the cooler side of the grill (position the legs closer to the fire). Cover and cook until the hens are golden brown, about 15 minutes.
Baste the hens with any extra jerk sauce, then turn them over to the direct-heat side of the grill; cook, uncovered, until the skin is dark brown and the meat is cooked through but still moist, 5 to 10 more minutes. (A thermometer inserted into the thickest part should read 160 degrees.) Set the hens aside for 5 minutes, then serve with the reserved jerk sauce.