Preheat. Preheat your grill to 325 degrees F and set it up for indirect cooking (meaning there is an area with no direct heat underneath the grates). If cooking on a smoker, use light hardwoods like alder, maple, pecan, or apple.
Make the stuffing. In a Dutch oven add sage sausage and brown over medium-high heat. Add in the butter followed by the diced onion and celery and cook until translucent, about 3-4 minutes. Remove the pan from the heat and stir in the sage, salt, pepper, apples, cranberries, bread, chicken broth, and eggs.
Stuff. Stuff the bread mixture inside the cavities of the Cornish hens. Add any additional stuffing to small ramekins or an 8-10 inch cast iron skillet.
Season. In a small bowl, combine the Chicken rub and mayonnaise. Pat the outside of the hens dry, then apply the wet rub, using a rubber spatula or a backside of a spoon to help distribute the seasoning paste.
Smoke. Place the pan of stuffing and the Cornish hens, breast side up, on the grill, and close the lid. Cook for 45-60 minutes. You want an internal temperature of at least 165 F in the thickest part of the breasts AND in the stuffing.
Serve. Remove the Cornish hens to your serving platter and rest (without covering) for 5 minutes before serving.