Absorption Refrigeration Cycles (ARC) represent a sustainable technology capable of effectively producing cold with modest energy consumption from waste heat or renewable sources. However, the right choice of working fluid pair absorbent–refrigerant is essential for the system to work properly. This contribution is devoted to analysing the performance of an ARC using a wide variety of refrigerants in combination with selected deep eutectic solvents (DES) as absorbents. Three choline chloride-based and one ionic liquid (IL)-based DESs as absorbers are combined with sixteen refrigerants. The PC-SAFT equation of state is employed to assess the thermophysical properties. Accurate modelling of the absorption cycle has revealed that the phase behaviour of the working mixture significantly constrains the temperature and pressure range within which the cycle can operate. Idealised ARCs are insufficient for accurately representing the capabilities and limitations of these systems. Of the sixty-four working pair mixtures, only eighteen are suitable for ARCs based on technical and thermodynamics criteria. The Coefficient of Performance (COP) has been updated with additional key performance indicators that consider environmental and safety factors. The maximum values of the COP for this mixture are around 0.92, while many options lie in ranges around 0.60. This comprehensive analysis helps establish a ranking of the best options. The results have shown that the IL-based DES using R227ea or R236ea is the most efficient system among all the systems studied, with performances of 0.92 and 0.74.