Is there a way/module to grant a role permission to list and edit terms in a specific vocabulary?
The only module I can think of is the Taxonomy access fix module, which has only a version for Drupal 7.
- adds 1 permission per vocabulary: "add terms in X"
- changes the way vocabulary specific permissions are handled
- changes the Taxonomy admin pages' access checks
- alters the vocabularies overview table to show only what you have access to edit or delete
The module does what native Taxonomy lacks: more specific Taxonomy permissions (and checking them correctly).
Both answers didn't work for me. "Taxonomy access fix" didn't work at all and the drupal permissions didn't work as expected. The only thing which is still having a chance to work is http://drupal.org/project/vppr - you may download a D7 version on the issues.
They can not change or delete the vocabulary itself, which is important. So they can not really administer the vocabulary but its terms.