This paper completes the constructive proof of the following result: Suppose p/q≥2 is a rational number, A is a finite set and f1,f2,···,fn are mappings from A to {0,1,···,p−1}. Then for any integer g, there is a graph G=(V,E) of girth at least g with https://static-content.springer.com/image/art%3A10.1007%2Fs00373-004-0596-6/MediaObjects/s00373-004-0596-6flb1.gif such that G has exactly n (p,q)-colourings (up to equivalence) g1,g2,···,gn, and each gi is an extension of fi. A probabilistic proof of this result was given in [8]. A constructive proof of the case p/q≥3 was given in [7].