Simple WordPress plugin that extends WP custom background feature to show a random image that change hourly. Images are selected via a checkbox on attachment edit screen. Wordpre for a WPSE anser, see http://wordpress.stackexchange.com/questions/141778/35541

gm-random-background.php

<?php 
/**
 * Plugin Name: GM Random Background
 * Description: Extends WP custom background feature to show a random image that change hourly
 * Plugin URI: http://wordpress.stackexchange.com/questions/141778/35541
 * Author: G. M.
 * Author URI: http://wordpress.stackexchange.com/users/35541/g-m
 *
 */
 
/*
Copyright (C) 2014 Giuseppe Mazzapica
 
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
 
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
 
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/


add_action( 'after_setup_theme', 'gmrb_background_image_size' );
add_action( 'after_setup_theme', 'gmrb_background_support' );
add_action( 'attachment_submitbox_misc_actions', 'gmrb_background_checkbox' );
add_action( 'update_post_meta', 'gmrb_background_checkbox_save', 20, 4 );
add_filter( 'theme_mod_background_image', 'gmrb_background_custom_filter' );

function gmrb_background_image_size() {
  // using WP 3.9 crop position
  // see https://codex.wordpress.org/Function_Reference/add_image_size#Crop_Mode
  $width = apply_filters( 'gmrb_background_width', 1920 );
  $height = apply_filters( 'gmrb_background_height', 1200 );
  $crop = apply_filters( 'gmrb_background_crop', array( 'center', 'center') );
  add_image_size( 'gmrb_background', $width, $height, $crop );
}

function gmrb_background_support() {
  if ( ! current_theme_supports( 'custom-background' ) ) {
    add_theme_support( 'custom-background' );
  }
}

function gmrb_background_checkbox() {
  wp_nonce_field('is_background', '_is_bkgrnd_n');
  $html = '<div class="misc-pub-section misc-pub-filename"><label for="is_bkgrnd">';
  $html .= '<input id="is_bkgrnd" name="_is_background" type="checkbox" value="1"%s />';
  $html .= '&nbsp;%s</label></div>';
  global $post;
  $is = get_post_meta( $post->ID, '_is_background', TRUE );
  printf( $html , checked(1, $is, FALSE), esc_html__('Background') );
}

function gmrb_background_checkbox_save( $mid, $pid, $key, $value ) {
  $post = filter_input(INPUT_SERVER, 'REQUEST_METHOD', FILTER_SANITIZE_STRING);
  if ( strtoupper($post) !== 'POST' ) return;
  if ( ! $key === '_wp_attachment_metadata') return;
  if ( ! check_admin_referer('is_background', '_is_bkgrnd_n') ) return;
  $is = (int) filter_input(INPUT_POST, '_is_background', FILTER_SANITIZE_NUMBER_INT);
  if ( $is === 1 ) {
    update_post_meta($pid, '_is_background', '1' );
  } elseif( get_post_meta($pid, '_is_background', TRUE ) ) {
    delete_post_meta($pid, '_is_background');
  }
}

function gmrb_background_get_random() {
  // first check transient
  $background = get_transient( 'my_background_random' );
  if ( empty( $background ) ) {
    // no transient, perform a query
    $args = array(
      'post_type' => 'attachment',
      'post_status' => 'inherit',
      'orderby' => 'rand',
      'posts_per_page' => 1,
      'meta_query' => array(
        array( 'key' => '_is_background', 'value' => 1, 'type' => 'NUMERIC' )
      )
    );
    $result = (array) get_posts( $args );
    if ( ! empty( $result ) ) {
      $attachment = array_shift( $result );
      $image =  wp_get_attachment_image_src( $attachment->ID, 'gmrb_background' );
      $background = ! empty( $image ) ? $image[0] : FALSE;
      if ( $background ) {
        // save transient for one hour
        set_transient( 'my_background_random', $background, HOUR_IN_SECONDS );
      }
    }
  }
  return $background;
}

function gmrb_background_custom_filter( $image ) {
  // do nothing on admin or core custom background interface will not work properly
  if ( is_admin() ) return $image;
  $random = gmrb_background_get_random();
  if ( $random && filter_var( $random, FILTER_VALIDATE_URL ) ) {
	  $image = $random;
  }
  return $image;
}

by using $post_type and limit the function gmrb_background_checkbox_save to post type "attachement", the above described issue can be fixed