Yes, you can put this in custom css.
To make a css rule affect only a certain page, just prefix any css declaration with the post id:
#post-1329 .slider_post {
background: url("image_URL");
}
That basically tells your browser to apply that background to any object of class .slider_post
only if it is part of an element with the id #post-1329
.
You would need to change to the correct post number, of course.