In Pokemon Black 2/White 2, Golurk have a 5% chance of holding Light Clay.
Those odds aren't great, so I would try this:
Get a Pokemon with Compound Eyes. I recommend a Joltik or Galvantula, because they are fairly easy to find. But you could do Yanma, if you have completed the Pokemon league.
Also get a Pokemon with Frisk, that can learn Theif/Trick. (Cover won't work because of Golurk's Ghost typing.) For this, I would recommend Banette. It can be found a little after Joltik and Galvantula, or in the same general area as Golurk. Get the TM Theif, which can be found in the Virbank Complex, right before the 2nd Gym.
Faint the Compound Eyes Pokemon, and put it at the first slot of you team. This gives the boost of Pokemon to be found with there respective items in the wild. (Now the 5% chance is a 20% chance.) Put the Frisk Pokemon with Trick/Theif second. Now, when you go into battle, the Frisk Pokemon should be sent out.
If Frisk activates, (It will say: (Pokemons name)'s Frisk found (Opponent)'s (Item)!) then you got a Pokemon with an item. Use Theif, and then run away. (Make sure that the Pokemon with Frisk isn't holding an Item before it uses Theif).
If Frisk doesn't activate, then run away and keep trying.
I haven't tried this in Pokemon White 2 yet, but I have in later generations. You could also try sending out the compound eyes Pokemon then switch to the Frisk Pokemon, which is what I do, but it does take a little more time.
Hope this helps! :)
Sources:
Experience and
https://www.serebii.net/itemdex/lightclay.shtml
https://www.serebii.net/itemdex/tm46.shtml