Soak wood chips in water for at least 1 hour.

Preheat an outdoor grill for indirect medium heat, about 350 degrees F (175 degrees C).

Combine sugar, salt, paprika, black pepper, and cayenne pepper in a small bowl. Place beer cans on a baking sheet. Spoon 1 teaspoon seasoning mix into each can. Be careful, this will make beer foam up and out of the can.

Rub each chicken with 2 tablespoons oil. Rub remaining seasoning mix over entire chickens, inside and out. Place each chicken upright over 1 beer can.

Drain wood chips; place with coals, in an aluminum pan, or under the grill grate according to manufacturer’s instructions.

Place cans with chicken directly on the grill. Close the lid and grill chicken until no longer pink, and juices run clear, about 1 1/2 hours. An instant-read thermometer inserted into the thickest part of thighs should read at least 165 degrees F (74 degrees C).

Remove chickens from the grill; discard the beer cans. Cover chickens with a doubled sheet of aluminum foil; rest in a warm area before slicing, 10 minutes.