Instead of serving a 404 Not Found error with the 404.php template, send a 403 Forbidden error and set $wp_query->is_403 and load 403.

Jesin A

Custom Error Pages

Create custom 401 and 403 error pages with any WordPress theme without writing a single line of code, set it up and forget it.

FAKTOR VIER

F4 Error Pages

With this simple plugin you can assign custom pages (with custom content etc.) as error pages. This works for 404 (page not found) and 403 (forbidden/ …

Presslabs

Site Protection

Site protection plugin for dev instances to avoid indexing by search engines. Doesn't allow access to the site without being logged-in.

Weston Ruter

This plugin is developed at <a href="http://www.shepherd-interactive.com/" title="Shepherd Interactive specializes in web design and development in Portland, Oregon" rel="nofollow ugc">Shepherd Interactive</a> 
for the benefit of the community. No support is available. Please post any questions to the <a href="https://wordpress.org/tags/private-page-forbidden?forum_id=10" rel="ugc">support forum</a>.
Instead of serving a 404 Not Found error with the <code>404.php</code> template, send a 403 Forbidden error and set <code>$wp_query->is_403</code> and load 403.php if it exists.
Provides a filter <code>forbidden_redirect</code> which if results in a non-empty filtered value will result in the user being redirected if attempting to visit a forbidden page; the default value is <code>""</code> (no redirect).
Useful with a filter which selectively prevents a private post from being forbidden, so that the page will not show up in the navigation and won’t be included in XML Sitemaps, for example.
<pre>function my_filter_private_posts($posts){ if(is_singular() && $posts[0]->post_status == 'private' && #Now optionally allow/disallow based on user session: in_array($_SERVER['REQUEST_URI'], (array)@$_SESSION['allowed_private_uris'])) ){ header('Cache-Control: private'); #Prevent proxies from caching this private page $posts[0]->post_status = 'publish'; } return $posts; } add_filter('posts_results', 'my_filter_private_posts');</pre>

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