Using a pair of poultry scissors, split the poussins down the breast side. Set the bird, backside down, on a clean work surface. Using the heel of your hand, press down to flatten the bird. Brush with olive oil. Season with salt and pepper.
Place flattened poussin on the heated grill. Cook over medium-low heat until the juices run clear when the thickest part is pricked with a two-pronged fork, about 30 minutes.