Solutions to repost categories into multisite blogs?

add_filter( 'the_posts', 'wpse138563_add_posts' );
function wpse138563_add_posts( $posts ) {
    if( ! is_multisite() ) {
        // if we're not using Multisite, bail
        return;
    }
    if( is_main_site() ) {
        // if we're in the root site, bail
        return;
    }
    $country = get_bloginfo( 'name' );
    // This assumes that the categories in your main site
    // have the same names as the country sites do
    if( $query->is_main_query() ) {
        // alter the main query
        switch_to_blog( BLOG_ID_CURRENT_SITE );
        $category = get_cat_ID( $country );

        // get the posts with the appropriate category
        $args = array(
            'category' => $category,
        );
        $more_posts = get_posts( $args );
        $posts = array_merge( $posts, $more_posts );

        restore_current_blog();
    }
    return $posts;
}

Untested. Hopefully this works, or at least provides you a starting point.

Caveat: The categories in your root site must have the same name as the site names of your subsites for this to work. ie, to have a post show up in a site named “Australia”, your category on domain.com must be named “Australia”.

References

• is_main_site()
• is_multisite()
• switch_to_blog()
• restore_current_blog()
• the_posts filter