Build discrete IIR from a transfer function which is not in terms of $s$
There exist genetic and evolutionary algorithms that attempt to guess and optimize a set of pole/zero placements that approximate an arbitrary frequency response.

There is also a algorithm called Frequency Domain Least Squares : http://www2.units.it/ramponi/teaching/DSP/materiale/ES_5_2.m 

The poles and zeros found can then be used to create an IIR recurance function.