Are Custom Taxonomy Templates Possible?

Custom Taxonomy templates are entirely possible, the order of the template loading is,

1. taxonomy-{sometax}-{someterm}.php – If the taxonomy were sometax, and
   taxonomy’s slug were someterm
2. taxonomy-{sometax}.php – If the taxonomy were sometax.
3. taxonomy.php
4. archive.php
5. index.php

This template hierarchy give you tons of control on how you want to alter the display of taxonomies as a whole, as a group or alone.
http://codex.wordpress.org/Template_Hierarchy

For example in your case you can create a template called taxonomy-sports.php and then customize it however you want using conditionals, template tags and functions.