Red Mage should not be a DPS. They are a jack of all trades but a master of none. personally this leaves only one option open. A tank. Red Mages use rapiers to attack. They have a small buckler shield. What they lack in heavy armor they make up for in parrys and dodges. While they can't hit hard they can keep the enemies attention with spells. Losing hate? Sling a lightning bolt from your rapier. Need to survive a strong hit? Use phalanx and dodge with ease. Stoneskin and cure would be usable but mainly for soloing.

Some staple moves that a Red Mage tank could have:
Doublecast: could cast a provoking spell twice or cast phalanx on self and healer.
Chainspell: makes any single target spell a AoE.
Multijab: medium damage from rapier. Manly used for keeping hate on bosses and for soloing.
Refresh: An MP and TP replenishing move.
This is my idea of a red mage. Every game I have ever played that had Red Mage I always thought, "It may take me forever to kill you but I'll never die."