What I've done in the past is to butterfly the game hens down the back, remove the backbone (reserve for stock), flatten the bird out, and marinate in some olive oil, rosemary, salt, pepper, and minced garlic. After a couple hours, grill over a medium fire until done. Be sure to get as much of the olive off as possible, as it will drip and flare. I can't remember how long I grilled them for, as it's been about 10 years since I made these.
I have made the hens on a stand that you use to make drunken chicken on. Takes the place of a beer can.This worked well. I have also done them by just letting them sit in a pan on the covered grill. I evo the hen and salt and pepper and put a garlic in cavity and tie legs together and after the hens start turning brown you can cover the legs with foil so as not to dry out.
Cornish Game Hens! They are the first success I had on the grill. It was over 25 years ago now. I had just purchased a Webber Smokey Joe barbecue that came with a small cookbook. It showed how to seperate the coals into 2 piles on either side of the grill for inderict heating and gave the approximate time per pound for those little beauties. I followed the directions and enjoyed the juciest poultry ever. I still follow the same directions, but use a meat thermometer to assure perfect results.
Place the thawed hens in hot water (110'F) to bring them to about room temperature. For a charcoal kettle style grill, pour in enough charcoal to cover the bottom in a single layer. Then seperate into equal piles on opposite sides. Sprinkle with lighter fluid liberally and light. The fluid will burn away by the time the coals are sizzling hot (look for flames coming up from the hot charcoal).
While the charcoal is heating, wash and then dry the hens with a paper towel. Brush the outside with softened butter, sunflower oil, or EVOO. Sprinkle with salt, balck pepper, or your favorite seasonings. Chop an onion into leaves and stuff these into the cavity. You can use a sauce if you want to, but it isn't required. The cooking technique is the same either way.
Insert a meat thermometer into the thickest part of the breast, pushing it in until it nearly touches the thigh joint. Make a drip pan from heavy aluminum foil, or use a disposable aluminum laof pan. Place the pan between the charcoal beds and fill halfway with water. Put the grilling grid back on the kettle and place the birds over the drip pan. Cover and immediately close all vents to the half-open position. Cook for about 10 minutes per pound, then check the thermometer. REmove the birds when the internal temp reads 155'F.
You can glaze the bird by brushing with a honey/lemon/water mixture if you so desire, or with your favorite barbecue sauce. You can brush with terryaki flavored mop as well. Just make sure that if you use a comercial barbecue sauce, you wait until the final 10 minutes of cooking time to prevent the sugar from scorching.
If you stuff the birds, with something like brown and wild rice, mishrroms, onions, etc., increase the approximate cooking time to 12 minutes per pound. Still remove at 155 internal temp though.
For a gas grill, you are going to mimick the indirect heating method by placing a suitable pot of water over the lit element, and the birds over the unlit element. Cover and follow the above directions.
You can also add hardwoods to either fire to give your gamehens a great flavor.
Follow these directions and I gauruntee that you will have the juciest Cornish Game Hens ever.