The Generalized Flory-Dimer (GFD) equation of state has been extended to fluids containing copolymers modeled as heteronuclear chains of freely-jointed tangent spheres that interact via a sire-site square-well potential. Compressibility factors are obtained for block, alternating and random copolymer fluids. The GFD theory for square-well copolymers requires expressions for the insertion factors of SW monomers In SW monomer mixtures, SW dimers in SW dimer mixtures, and SW heteronuclear dumbbells in SW heteronuclear dumbbell fluids. These insertion factors are obtained using recently-derived perturbation-theory-based equations of state. The effects of variations in composition, segment size ratios, and well-depth ratios on the compressibility factor are studied. The predictions of the Generalized Flory-Dimer theory are compared to compressibility factors obtained from discontinuous canonical molecular dynamics simulation. The Generalized Flory-Dimer theory accurately predicts the compressibility factors of square-well copolymer fluids for a variety of cases including those in which the size ratio and well-depth ratio of the two components are different.