Now, understand that I don’t know for sure, but I bet I am right.
The sides of the hole in the gemstone are rough. It abrades the wire
into a powder that looks black because it is divided so finely. In
other words, tarnish is not really your problem. One solution would
be to polish the hole in the gemstone. I doubt that this would be
worth your time. Another solution would be to line the hole with a
clear material. I suggest plastic. I don’t know where to find it, but
a tiny plastic tube might do the trick. Finally, make your own tube.
In other words, paint the part of the wire that goes in the stone
with epoxy. Then you will have a barrier between the wire and the
rough sides of the hole. This would prevent the abrasion.