How to display childrens custom fields?

Change the line

<?php echo apply_filters('the_content', get_post_meta($page->post_content, 'custom_tagline')); ?>

to

<?php echo apply_filters('the_content', get_post_meta($page->ID, 'custom_tagline')); ?>

See http://codex.wordpress.org/Function_Reference/get_post_meta

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