I have been using the Target Brand Feminine Wash to was my Diva Cup for a couple cycles now and am very happy with it.. I have not had any odor problems with the cup or irritation issues with my bits. It is gentle, rinses clean, and is Ph balanced. Best part is that it is under $2!
ETA - Ingredients: purified water, ammonium laureth sulfate (surfactant), decyl glucoside (a mild non-ionic surfactant), disodium cocoamphodiacetate (Extremely mild, amphoteric surfactant), cocamidopropyl betaine (amphoteric detergent), coco-glucoside (gentle detergent derived from coconuts), glyceryl oleate (emulsifier), citric acid (preservative), disodium edta (chelating agent and a viscosity adjuster), methylchloroisothiazolinone (preservative ), methylisothiazolinone (powerful biocide and preservative), fragrance (perfume), FD&C red #33 (dye) & FD&C blue #1(dye)