Why is 2nd largest rear cog making clicking noise?
It would be one of a few things:


The rear derailleur is not center aligned on the rear cog when in that gear. Take a look at the cog and derailleur gear alignment dead on from the rear when in the noisy gear and look for vertical alignment. If it is misaligned it can be ajusted with the barrel adjuster.
The chain is not clearing the front derailleur guard when in this gear. Look at it from the top down when in the noisy cog and ensure no rubbing between the chain and derailleur guard. If there is rubbing the limit screws can be adjusted
The cog is damaged in some way causing some sort of misalignment


The problem with the first two possibilities is that I'd expect the noise to persist in the 1st cog as well.