Dear dmfzw,
The default post_type parameter for the get_pages function is "page", I've set it to "countries" and it is working fine. The code to get the childrens now is:
$pageChildren = get_pages(array( 'child_of' => get_the_ID(), 'post_type' => 'countries' ));
Please let me know if you are satisfied with my answer and if I can help you with any other questions you might have.