This work developed new electrocatalysts for direct alcohol oxidation fuel cells (DAFCs) by using graphene and reduced graphene oxides (GO and rGO) as supporting nanomaterials for copper–nickel (CuNi) nanocomposites. The manufacture of CuNi, CuNi-GO, and CuNi-rGO nanocomposites was realized through the adaptation of Hummer’s method and hydrothermal techniques, with subsequent analysis using a range of analytical tools. The electrocatalytic behavior of these materials in DAFCs, with methanol and ethanol as the fuels, was scrutinized through various methods, including cyclic voltammetry, linear sweep, chronoamperometry, and electrochemical impedance spectroscopy. This investigation also assessed the stability and charge transfer dynamics. The rGO-based CuNi nanocomposite demonstrated a remarkable performance boost, showing increases of approximately 319.6% for methanol and 252.6% for ethanol oxidation compared to bare CuNi. The integration of silver nanoparticles into the Ag-CuNi-rGO electrode led to a current density surge to 679.3 mA/g, which signifies enhancements of 254.2% and 812.6% relative to the CuNi-rGO and CuNi electrodes, respectively. These enhancements are ascribed to the augmented densities of hot sites and the synergistic interactions within the nanocatalysts. The findings underscore the potential of Ag and rGO as effective supports for CuNi nanocomposites, amplifying their catalytic efficiency in DAFC applications.