Is there a limited supply of Titanite in Dark Souls 2? I know that in the first game, you could find merchants that never ran out of Titanite Shards but the only merchants I've found so far have a limited supply.
There is an unlimited supply of all forms of Titanite.
All Titanite up to Chunks are sold in unlimited supply by the NPC Stone Trader Chloanne.
Chloanne is found in Harvest Valley, until you talk to her so much she runs out of new things to say, in which case she’ll go to Majula. You can pretend it’s your fault.
Get unlimited Titanite Shard by clearing Iron Keep, unlimited Large Titanite Shard by clearing Drangleic Castle, and unlimited Titanite Chunks by clearing the Undead Crypt. When you get through the final boss, Titanite becomes infinite.
The only one that is left is Titanite Slab, which can be farmed off of the stone soldier in Drangelic Castle.
Although not part of the regular titanite upgrade path, Twinkling Titanite can be farmed off of the Archdrakes in Shrine of Amana. Alternatively they can be Acetic farmed in Dragon Aerie(5x?) and the Giant Memories(2x).