1. Combine wood chips and contents of one can of the beer in a small foil pan. Let stand 1 hour.
2. For spice rub, combine paprika, onion powder, cumin, salt, red and white pepper, and sugar in a small bowl. Divide and sprinkle 1 tablespoon rub into the cavity of each chicken. Sprinkle remaining rub evenly over surface of chickens. If desired, place each chicken in a large plastic storage bag, seal and refrigerate overnight. Open the remaining 3 beer cans and stand on a work surface with chicken. Punch 2 additional holes in top of each can. Holding each chicken upright, place it over the can so that the can goes into main cavity. Pull chicken legs forward to form a sort of tripod, allowing the chicken to sit upright over can.Prepare grill for indirect grilling. For gas::
3. Drain wood chips; place chips in a small foil pan in front left-hand corner of the grill. Add 1/2 cup water. Place a large disposable foil pan in center of bottom grate. Add 2 cups water. Replace top cooking grate. Close lid and heat burners on medium, 10 to 15 minutes. To grill, adjust burner controls. Be sure to position chickens in center of grill and turn off heat source directly under the chicken. (For triple-burner grill, turn center burner off.) Cover and grill 60 to 70 minutes (reduce heat if necessary to maintain heat at 350 degrees F.) until an instant-read meat thermometer inserted in thigh registers 180 degrees F.For charcoal briquettes::
4. Open all vents. Build two equal piles of briquettes (30 to 50 total, depending on the size of your grill) opposite each other on bottom grate near the grate edge. Ignite and burn briquettes 25 to 30 minutes until coals are covered with a light coating of gray ash. Place a disposable foil drip pan in center of bottom grate. Add 2 cups water. Transfer chickens to center of grate over drip pan. Drain wood chips and add 1 cup chips to top of each pile of hot briquettes. Cover and grill 60 to 70 minutes, until an instant-read meat thermometer inserted in thigh registers 180 degrees F.
5. Carefully remove chickens and cans from grill. Insert a large fork into the neck of each chicken and lift the chickens, holding each can with an oven mitt to remove from chicken. Transfer to a serving platter.