The effect of Co doping on the oxygen disordering and superconducting transition temperature in YBa₂Cu_3-yCo_yO_6+x has been studied experimentally and by Monte Carlo simulations. Samples with Co doping levels, 0≤y≤0.5, have been prepared and their superconducting transition temperatures have been determined by DC resistivity and ac susceptibility measurements. Structural ordering phenomena have been studied by neutron powder diffraction and EXAFS measurements. Model calculations based on a modified version of the so-called ASYNNI model, which takes into account the increased probability of excess oxygen around the Co sites, have been carried out and compared with the experimental results of oxygen coordination number around the Co atoms and the oxygen stoichiometry in the basal Cu_1-yCo_yO_x plane of the structure. Using a previously established minimal model relating the superconducting transition temperature, T_c(x), in the undoped material to the presence of specific ordered oxygen domains we show that the detrimental effect on T_c(y) by Co doping is a result of oxygen disordering.