I think the_terms() is what you’re looking for. Apologies if I’ve misread your post.
http://codex.wordpress.org/Function_Reference/the_terms
The the_terms() function is used to return a list of terms for a given taxonomy of a specific post.
You should be able to ignore the last 3 parameters, just passing the first 2 should be fine – the post’s ID and the name of your custom taxonomy.
Try this..
<?php the_terms( $post?>ID, 'taxonomy_name', '', '', '' ); ?>
edit – for some reason there’s a question mark showing up above, it’s supposed to be the following without spaces..
$ post – > ID