Composite edible coatings based on hydroxypropyl methylcellulose (HPMC), as a polymeric phase, and oleic acid (OA) or beeswax (BW), as a hydrophobic phase, were formulated with different food additives as antifungal ingredients. HPMC–OA coatings containing 2% (w/v) sodium benzoate (SB), 1% ammonium carbonate (AC), 1% potassium carbonate (PC), 1% potassium bicarbonate (PBC), 1% sodium bicarbonate (SBC), 1% potassium silicate (PSi), 0.1% sodium methyl paraben (SMP) or 0.1% sodium ethyl paraben (SEP), and HPMC–BW coatings containing 2% sodium propionate (SP), 2% PBC, 2% SB or 0.1% SEP were evaluated for the control of Alternaria black spot (ABS) on Diospyros kaki Thunb. ’Rojo Brillante’ persimmons artificially inoculated with Alternaria alternata. After 14 days of incubation at 20 °C, HPMC–OA coatings formulated with PBC, PC or SEP were the most effective to reduce ABS incidence (61, 54, and 36% reduction, respectively, concerning uncoated control fruit) and severity (28, 12 and 22% reduction, respectively), while only HPMC–BW coatings formulated with SEP significantly reduced ABS incidence (50% reduction) and severity (36% reduction). HPMC–OA and HPMC–BW coatings containing 2% PBC or 0.1% SEP were selected to evaluate their effect on the weight loss, firmness and respiration rate of healthy ‘Rojo Brillante’ persimmons cold-stored at 1 °C and 90% relative humidity (RH) for 15 and 30 days, followed by 7 days of shelf life at 20 °C. HPMC–BW coatings were more effective in reducing fruit weight and firmness losses than HPMC–OA coatings, while all antifungal coatings significantly reduced fruit respiration. Overall, the HPMC–BW edible coating that contains SEP could be a promising postharvest treatment to control ABS and maintain the quality of cold-stored ‘Rojo Brillante’ persimmons.