There is no player-obtainable raw gem named Tanzanite, so there are no craftable designs for them. However, there are a number of cut tanzanite gems that drop from instance bosses in Heroic mode.

Purple, match UI-EmptySocket-Red red or UI-EmptySocket-Blue blue sockets.
Name Effect Source (Heroic Bosses)
[Blessed Tanzanite] +6 Spell Power +6 Stamina Sethekk Halls
[Brutal Tanzanite] +10 Attack Power +6 Stamina The Botanica
[Defender's Tanzanite] +5 Parry +6 Stamina The Mechanar
[Fluorescent Tanzanite] +6 Spell Power +4 Spirit Blood Furnace
[Glowing Tanzanite] +6 Spell Power +6 Stamina The Black Morass
[Imperial Tanzanite] +5 Spirit +5 Spell Power The Botanica
[Regal Tanzanite] +5 Dodge +6 Stamina Shadow Labyrinth
[Royal Tanzanite] +6 Spell Power 2 Mana per 5 seconds The Slave Pens
[Shifting Tanzanite] +5 Agilty +6 Stamina The Steamvault
[Sovereign Tanzanite] +5 Strength +6 Stamina Shattered Halls