There is no Cu(III) btw.
Oh yes, there is. Copper (III) compounds can be made by mixing Na-DCCA or alkaline TCCA with copper (II) sulfate. These compounds have a beautiful purple color, very uncommon for copper.
This is possible due to the very strong oxidizing properties of the solution of Na-DCCA (sodium dichloro isocyanuric acid, Na-C3N3O3Cl2). Copper (III) compounds also are said to be achievable by oxidation with concentrated hypochlorites in the cold, but I have not been able to prepare these copper (III) compounds.