Methods for making multi-piece golf balls comprising at least one component made of ethylene-propylene diene copolymer (EPDM) rubber and the resulting balls are provided. The multi-piece golf ball includes a cover, preferably a dual-cover having inner and outer cover layers. The outer cover is preferably made of a liquid rubber composition based on liquid EPDM rubber. In one version, the ball sub-assembly is dipped in a bath containing liquid EPDM rubber to form the outer cover. In another version, a casting method is used and the liquid EPDM rubber is dispensed into mold cavities to form the outer cover. The inner core of the ball may be made of polybutadiene rubber and the outer core layer may be made of EPDM rubber. The resulting golf ball has high resiliency, a soft feel, and good weatherability.