Bio-composite coatings consisting of poly(3,4-ethylenedioxythiophene) (PEDOT) and tyrosinase (Ty) were successfully electrodeposited on conventional size gold (Au) disk electrodes and microelectrode arrays using sinusoidal voltages. Electrochemical polymerization of the corresponding monomer was carried out in the presence of various Ty amounts in aqueous buffered solutions. The bio-composite coatings prepared using sinusoidal voltages and potentiostatic electrodeposition methods were compared in terms of morphology, electrochemical properties, and biocatalytic activity towards various analytes. The amperometric biosensors were tested in dopamine (DA) and catechol (CT) electroanalysis in aqueous buffered solutions. The analytical performance of the developed biosensors was investigated in terms of linear response range, detection limit, sensitivity, and repeatability. A semi-quantitative multi-analyte procedure for simultaneous determination of DA and CT was developed. The amperometric biosensor prepared using sinusoidal voltages showed much better analytical performance. The Au disk biosensor obtained by 50 mV alternating voltage amplitude displayed a linear response for DA concentrations ranging from 10 to 300 μM, with a detection limit of 4.18 μM.