In this study, cobalt-nickel (Co-Ni), cobalt-iron (Co-Fe), cobalt-iron-manganese (Co-Fe-Mn), cobalt-iron-molybdenum (Co-Fe-Mo), and cobalt-zinc (Co-Zn) coatings were studied as catalysts towards the evolution of hydrogen (HER) and oxygen (OER). The binary and ternary Co coatings were deposited on a copper surface using the electroless metal plating technique and morpholine borane (MB) as a reducing agent. The as-deposited Co-Ni, Co-Fe, Co-Fe-Mn, Co-Fe-Mo, and Co-Zn coatings produce compact and crack-free layers with typical globular morphology. It was found that the Co-Fe-Mo coating gives the lowest overpotential of 128.0 mV for the HER and the lowest overpotential of 455 mV for the OER to achieve a current density of 10 mA cm−2. The HER and OER current density values increase 1.4–2.0 times with an increase in temperature from 25 °C to 55 °C using the prepared 3D binary or ternary cobalt coatings for HER and OER. The highest mass electrocatalytic activity of 1.55 mA µg−1 for HER and 2.72 mA µg−1 for OER was achieved on the Co-Fe coating with a metal loading of 28.11 µg cm−2 at 25 °C.