A general irreversible cycle model of a magnetic Ericsson refrigerator is established. The irreversibilities in the cycle model result from the finite-rate heat transfer between the working substance and the external heat reservoirs, the inherent regenerative loss, the additional regenerative loss due to thermal resistances, and the heat leak loss between the external heat reservoirs. The cycle model is used to optimize the performance of the magnetic Ericsson refrigeration cycle. The fundamental optimum relation between the cooling rate and the coefficient of performance of the cycle is derived. The maximum coefficient of performance, maximum cooling rate and other relevant important parameters are calculated. The optimal operating region of the cycle is determined. The results obtained here are very general and will be helpful for the optimal design and operation of the magnetic Ericsson refrigerators.