In a small bowl, combine all of the ingredients for the rub and mix well.
Pop the tabs off the root beer cans. Pour half the root beer from each can into a large bowl and reserve for the sauce. Using a church-key style can opener, make 2 additional holes in the top of each of the cans. Set the cans of root beer aside.
Remove the packet of giblets (if any) from the body cavities of the hens and set aside for another use. Remove and discard the fat just inside the body and neck cavities. Rinse the hens, inside and out, under cold running water and then drain and blot dry, inside and out, with paper towels. Season the inside of each bird (neck and body cavity) with 2 teaspoons of the spice rub. Rub the outside of the hens with the oil and season with an additional 2 teaspoons of the rub.
Set up the grill for indirect grilling and preheat to medium. If using a charcoal grill, place a large drip pan in center. If using a gas grill, place all the wood chips or chunks in the smoker box or in a smoker pouch and preheat on high until you see smoke, then reduce the heat to medium.
Holding a game hen upright, with the opening of the body cavity at the bottom, lower the hen onto a root beer can so the can fits into the cavity. It will be a tight fittighter than a chickenbut with a little twisting and jiggling, you should be able to work the can into the cavity. Repeat with the remaining hens, then tuck the wing tips behind the hens' backs.
When ready to cook, if using a charcoal grill, toss all the wood chips on the coals. Line up the hens in the center of the hot grate, over the drip pan, away from the heat. Take special care to balance the hens securely. The legs won't reach the grate, so you'll have to balance the hens solely on the cans. Cover the grill and cook the hens until the skin is a dark golden brown and very crisp and the meat is cooked through (about 180° on an instant-read meat thermometer inserted in the thickest part of a thigh), 40 to 60 minutes. If the hens start to brown too much, loosely tent them with aluminum foil.
Using tongs, carefully transfer the hens (grab the bird by the root beer can just under the butt) in an upright position on the root beer cans to a platter and present them to your guests. Let rest for 5 minutes, then carefully lift the hens off the cans. Take care not to spill the hot root beer. Serve one hen per person with the Root Beer Barbecue Sauce.
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