There is no specific template for child pages, but you can do this pretty easily with the get_template_part() function.
First create a file called "content-child.php".
Second create a file called "content.php".
Next, inside of page.php, place this:
<?php
if( $post->post_parent !== 0 ) {
get_template_part('content', 'child');
} else {
get_template_part('content');
}
?>
Anything that you want displayed on a child page will be placed inside of content-child.php. Anything you want displayed on non-child pages will be placed in content.php.