After decades of using reliable synthetic refrigerants, it is now necessary to look for their low-GWP climate-friendly safe alternatives. This paper summarizes a search for the best substitutes to commonly used refrigerants and their blends to be used in vapor compression air conditioning systems and temperature conditions typical for a moderate climate. 24 pure refrigerants (including several modern HFOs) were combined (using REFPROP10’s mixing functions) in binary and ternary compositions (at 10% mass fraction adjustments) producing 44 915 potential combinations. This broad database was screened on the basis of theoretical COP, specific cooling capacity, and volumetric cooling capacity which were obtained through simulations of an ideal cycle with the temperature of evaporation 0 °C, condensation 38 °C and superheating 10 K. Resulting blends were then further sieved on the basis of Global Warming Potential (GWP), discharge temperature, temperature glide, and flammability. The refrigerants that produced the highest COP under the above screening criteria are: R13I1 and its blends. The COP was 4.94, but R13I1 is hard to acquire in necessary quantities. The other high-COP/low-GWP blends contain R1234ze(Z) and/or R1233zd(E), but the evaporator would work below atmospheric pressure. Further screening returned R152a/R1234ze(E) [0.7/0.3 mass ratio] as the best refrigerant blend for the air conditioning purposes. It is inexpensive, belongs to flammability group 2L, and the ideal refrigeration cycle yields a theoretical COP of 4.861.