Redirect private page 404 errors to the login screen with a message

functions.php

<?php

add_action( 'wp', 'my_private_page_404' );

function my_private_page_404() {
	$queried_object = get_queried_object();
	if ( isset( $queried_object->post_status ) && 'private' == $queried_object->post_status && !is_user_logged_in() ) {
		wp_safe_redirect( add_query_arg( 'private', '1', wp_login_url( $_SERVER['REQUEST_URI'] ) ) );
		exit;
	}
}

add_filter( 'login_message', 'my_private_page_login_message' );

function my_private_page_login_message( $message ) {
	if ( isset( $_REQUEST['private'] ) && $_REQUEST['private'] == 1 )
		$message .= sprintf( '<p class="message">%s</p>', __( 'The page you tried to visit is restricted. Please log in or register to continue.' ) );
	return $message;
}