It is possible to create coupons. I got it working both from a php script and using the developer playground at https://developer.bigcommerce.com/console
$coupon = array('name' => 'FJKDJFKD', 'type' => 'percentage_discount', 'amount' => 50.0, 'code' => 'JFKDFE', 'enabled' => true, 'applies_to' => array('entity' => 'products', 'ids' => array(32)), 'shipping_methods' => array());
print_r($coupon);
Screenshots from the playground -