Preheat the oven to 500 degrees.
Rinse the poussins and season the cavities with salt and pepper. Rub each with 1/4 teaspoon olive oil. Fill each cavity with a lemon wedge, 2 sprigs each of thyme and marjoram, and 1 crushed garlic clove.
Loosen the skin from the breast of each poussin. Slide a sprig each of thyme and marjoram between the skin and the breast. Spoon the Cognac (1/2 tablespoon per bird) into the breast pockets of each poussin. Truss with kitchen string.
On a roasting rack set in a roasting pan, roast for 30 minutes, or until the juices run clear when the thigh is pierced with a fork.