Whitelist a Wordpress custom post type for use with the Jetpack JSON API using the `rest_api_allowed_post_types` filter. See http://developer.wordpress.com/docs/api/1/get/sites/%24site/posts/

gistfile1.php

function allow_my_post_types($allowed_post_types) {
	$allowed_post_types[] = 'my_post_type';
	return $allowed_post_types;
}

add_filter( 'rest_api_allowed_post_types', 'allow_my_post_types');