The only dungeon you may visit to boost your Consortium reputation is Mana Tombs, and only in Heroic setting after the first time you clear the place for its quests.

What gives the consortium rep?

The Consortium is a Nagrand-based faction in TBC. Most of the reputation with them is obtained by killing Ethereals in Netherstorm, as well as by doing quests and through repeatable turn-ins. The Consortium offers a variety of powerful pre-raid items, as well as many profession patterns.

How do you get a consortium revered?

Just collect Kurenai off of Ogre kill exp and save the beads for Consortium. Grinding the requisite mob rep for Kurenai will generate enough beads to get way into Revered for Consortium.