Summary: A numerical method is developed to treat the statistical equilibrium model of coherent structures in two-dimensional turbulence. In this model the vorticity, which fluctuates on a microscopic scale, is described macroscopically by a local probability distribution. A coherent vortex is identified with a most probable macrostate, which maximizes entropy subject to the constraints dictated by the complete family of conserved quantities for incompressible, inviscid flow. Attention is focused on the special case corresponding to vortex patches, and a simple, robust, and efficient algorithm is proposed in this case. The form of the iterative algorithm and its convergence properties are derived from the variational structure of the statistical equilibrium problem. Solution branches are computed for the shear layer configuration, and the results are interpreted in terms of the dynamical phenomena of rollup and coalescence.