Due to the intermittent nature of the solar radiation, the day-long continuous production of cold is a challenge for solar-driven adsorption cooling systems. In the present study, a developed solar-powered adsorption cooling system is introduced. The proposed system is able to produce cold continuously along the 24-h of the day. The theoretical thermodynamic operating cycle of the system is based on adsorption at constant temperature. Both the cooling system operating procedure as well as the theoretical thermodynamic cycle are described and explained. Moreover, a steady state differential thermodynamic analysis is performed for all components and processes of the introduced system. The analysis is based on the energy conservation principle and the equilibrium dynamics of the adsorption and desorption processes. The Dubinin–Astakhov adsorption equilibrium equation is used in this analysis. Furthermore, the thermodynamic properties of the refrigerant are calculated from its equation of state. The case studied represents a water chiller which uses activated carbon–methanol as the working pair. The chiller is found to produce a daily mass of 2.63 kg cold water at 0 °C from water at 25 °C per kg of adsorbent. Moreover, the proposed system attains a cooling coefficient of performance of 0.66.