I am trying to evaluate how much capital cost would be required to set up a refrigeration system that would be required to remove say about x kWh of energy or provide about y kW of cooling.
In refrigeration systems, the control system is what allows the efficiency to be set. The size of the system is by thermal load. You need a base with variable speed motors and a control system that adjusts to the efficiency you want. So the base investment without a control system takes you to a base efficiency value in terms of $/ton. Better ranges of efficiencies would be achieved with investment in flow / temperature measurement equipment and variable speed drives in electric motors. That may be an approach
In peter + tmmmerhaus, 4th ed. 1991, there is a graph on page 811.In Baasel 2nd edition, pagee 533 give s equations for refrigeration costs (1987). In Towler, 2008 there is is a correlation on page 320.In Walas, 1988, there is a correction on page 688. I'm sure there is probably some in Turton. You might also look a Chem Eng Magazine, Matche.com and try looking into ASHRAE documentation.