Yes, the oozing resin turns black after a while. I'm not sure if it's UV radiation or some kind of fungus or bacteria that convert it to something tar-like.
Time will fix that, but it takes about a year.
Sulfuric acid will stain wood black through oxidation, but it takes a strong concentration to do so and it happens almost immediately (or it will turn into fire). Iron oxide will also turn black. But iron sulphate is usually so diluted that it shouldn't discolor anything.
I would apply lime sulfur again, it should go white in a few days.