Depends on what your intent is. How easily do you envision the party solving the problem? Do they need to discover, through research and /or experiment, what the vulnerability is? If so, it can be anything....ashes from a funeral pyre, tears shed in sorrow, kryptonite.
Or is the weakness common knowledge, and the party simply needs to make sure they have the item with them? In that case, cold iron works as well as anything else.
Or is it something they must discover in the heat of battle, by observation, logic or plain luck? In that case it should be something they actually do have. Maybe human(oid) blood acts as a poison, so they have to first blood the weapon (taking 1 point of damage and using a minor action) before each hit.
A related question... if you make the weakness hard to discover or costly to acquire, can the party win without it? Is the choice to use it or not meaningful? Is there a downside? If the weakness is well known and plentiful, every adventurer will carry it, and so the regeneration ability becomes a waste of ink, except as backstory.