Dating methodology for the Vishnu Schist

To address the issue of carbon dating, the reason why carbon dating is not relevant in this discussion of the grand canyon is that the half-life of carbon 14 (5,730 years) is much too short to measure anything as old as most rocks. Carbon 14 is only good for about 50,000 years before there's too little of it present in the material to reliably measure. The other reason why you wouldn't use carbon to date rocks is that rocks usually don't contain all that much carbon, carbon dating is used for dead things like pieces of paper or paint or wood from archaeological sites.
The most common decays used are potassium-argon (HL of 1.3 billion years) and uranium-lead (the two isotopes of uranium (238 and 235) decay to different isotopes of lead (207 and 206) with HLs of 700 million and 4.5 billion).