Que tal:
$query = "SELECT p1.id,
(SELECT COUNT(1)
FROM post_table p2
WHERE p2.parent_id = p1.id) as num_children
FROM post_table p1
WHERE p1.parent_id = 0";
ou se você colocar um alias no p1.id, você pode dizer:
$query = "SELECT p1.id as p1_id,
(SELECT COUNT(1)
FROM post_table p2
WHERE p2.parent_id = p1.id) as num_children
FROM post_table p1
WHERE p1.parent_id = 0";