Absorption heat pumps (AHPs) for thermal cooling show great potential in utilizing renewable and waste heat towards carbon neutrality. AHPs using ionic liquids (ILs) as absorbents have attracted considerable attention for avoiding the shortcomings of traditional working fluids. To develop absorption technologies with high efficiency, compactness, and flexibility, a multi-criteria approach coupling the property models based on machine learning and UNIFAC methods, cycle models, and heat exchanger models is proposed to screen the optimum refrigerant/ILs. In terms of cycle performance, heat transfer performance, hydraulic resistance, and applicable range, the comprehensive performance of 214 novel refrigerant/ILs is estimated to identify suitable candidates. Six indicators are selected to compare the working pairs comprehensively: H2O/[OMIM][OAc] performs the best in terms of coefficient of performance (0.815), pumping power (0.071 W), and supply-side applicable operating ratio (76.8%), while NH3/[DBIM][Tf2N] yields the lowest saturation temperature drop (0.157 K) and the highest demand-side applicable operating ratio (64.9%). Within the studied IL-based working fluids, NH3/[DBIM][Tf2N] in the generator exhibits the highest heat transfer coefficient of 0.476 kW/(m2·K). Considering the trade-off between heat transfer performance and hydraulic resistance, satisfactory solution velocities are recommended for different working fluids with a saturation temperature drop limit of 2.2 °C. Based on the Pareto optimization, H2O/[OMIM][OAc] is highly recommended for industrial applications because of its crystallization-free nature, high COP, and compact system size. The proposed multi-criteria approach achieves large-scale screening of optimum ILs for highly efficient, compact, and flexible thermal cooling.