Per this 1991 study "Effect of Additives on Pyrite Oxidation" by By G. W. Reimers and D. F. Franke, apparently the presence of chloride reduces pyrite oxidation with air/oxygen.
The cited products of this air oxidation includes soluble ferrous sulfate and also sulfur dioxide. The latter forms bisulfite with water, and with transition metal tap water (with increased ferrous content) upon vigorous aeration, the sulfite radical is introduced (from Fenton hydroxyl radicals acting on bisulfite). This sulfite radical can apparently rapidly react with oxygen creating a long chain of reactive species (see, for example, this ScienceDirect account and even more recent work by Rivas discussed here).
So, do not use nitrate or chloride source, just vigorous aeration (like with an air pump) of tap water containing the pyrite should suffice especially with optional strong sunlight.