For a charcoal grill, place a 9-by-13-inch aluminum pan in the center of the bottom rack of the grill. Light briquettes in a charcoal chimney according to instructions. When the briquettes are covered with gray ash, arrange them on the bottom rack around the pan. For a gas grill, set a 9-by-13-inch disposable aluminum pan under the grate on one side of the grill. Turn the gas to medium-low on the side without the pan. (Leave the side with the pan off.) For both types of grill, add the top rack.
In a bowl, mix the sugar, paprika, salt, pepper, onion powder, cayenne and oregano. Sprinkle 2 tsp. rub inside the cavity of the chicken. Starting at the neck end, gently slide your fingers under the skin to separate it from the flesh. Pat 1 tbsp. rub onto the flesh, under the skin. Drink half the beer. (Yes, really!) Pour 2 tbsp. rub into the can; place on a baking sheet. Lower the chicken onto the can, filling the cavity; use the can and the legs to stabilize the bird so that it stands upright.
Transfer the chicken to the grill; lift it off the baking sheet and place it on the rack over the drip pan, using the can and the legs to prop it up; cover. For a charcoal grill, insert an instant-read thermometer into a vent in the lid. Cook the chicken, maintaining the heat at about 250 degrees , until an instant-read thermometer registers 165 degrees when inserted into the thickest part of the thigh, about 2 hours. (If the temperature drops below 250 degrees on a charcoal grill, prepare more briquettes and replenish as needed.)
Carefully lift the chicken off the can and transfer to a cutting board. Let the chicken rest 10 minutes before carving.