Co- and Cu-doped ZnO of nominal composition Zn_0.95Co_0.05O and Zn_0.94Co_0.05Cu_0.01O were synthesized by a co-precipitation method in organic media. Rietveld refinement of X-ray diffraction data of the samples annealed at 725 K showed that they are single phase without any secondary phases. DC magnetization measurements of samples with Cu co-doping (Zn_0.94Co_0.05Cu_0.01O) as a function of field at room temperature showed a ferromagnetic signature while the samples without Cu co-doping (Zn_0.95Co_0.05O) are paramagnetic in nature. Both the samples heated at 1075 K are found to be paramagnetic at room temperature. Resistivity measurements above room temperature clearly showed a semiconducting behavior with a decreased resistivity value for Zn_0.94Co_0.05Cu_0.01O compared to Zn_0.95Co_0.05O and ZnO, confirming additional carriers in Zn_0.94CO_0.05Cu_0.01O due to Cu co-doping. Our results are in agreement with a recent computational study that doping additional carriers are necessary for realizing room temperature ferromagnetism in Co-doped ZnO.