I would watch your PH. Pyrite is common in some slates and when it oxidizes it can raise the pH in the water. The FeS2 decomposes in water in the presences of oxygen to Fe ions, and SO4 ions and Hydrogen ions. Essentially forming Sulfuric Acid. Sulfuric Acid is common in low concentration in many environments so is not necessarily bad for your fish. If your water does not become significantly more acidic it is likely ok.
Overall I don't think the rock will cause issues if the staining is just on the surface. The pyrite or iron depositions on slate is often only along the bedding or cleavage planes where the redistribution of minerals during the rock forming process occurs.