If you add default StumbleUpon Button code on WordPress Post page(Single.php) it will work. but this wont work if you would like to use this on Home Page(index.php) it wont work. Like i did tried to add this on TheTechJournal.com‘s home page. It was not woking, showing only home page view count. Then i altered the code with parmalink.
Use This code
<script src=”http://www.stumbleupon.com/hostedbadge.php?s=5&r=<?php the_permalink() ?>”></script>