I've tried using the page-node-2.tpl.php but it hasn't worked... Is there something I'm missing?
I'm new to Drupal, but I think it might have something to do with not having a template.php in my themes directory?
See http://drupal.org/node/1089656 for template file name conventions. Note that there are two dashes (--) in between page and node and 2.
Also remember to clear your cache so that Drupal recognizes the new files and/or paths.