Jacob Chappell on "show 1 post in parent category"

I can only show you the WP_Query argument because that's what I use. You can exclude posts from a particular category. In this case, you'd want to exclude all posts from that child category.

If Parent Cat 1 has a category ID of 1 and
Child Cat 1 has a category ID of 2 then:

'category__not_in' => array( 2 )

would be the parameter for WP_Query. You can view the category parameters for WP_Query here.

You could pass additional arguments to that array if you wanted to exclude other categories as well.