A generalization of integral equation theory of simple liquids is used to study the structure and thermodynamics of a monolayer of spherical colloidal particles having a continuous distribution f(sigma) of diameters sigma. The quasi-two-dimensional fluid is modeled using both a repulsive Yukawa potential to represent charged hard spheres (with attendant charge polydispersity) and a Lennard-Jones potential to represent soft spheres with an effective attractive well. The numerical solution of the integral equations makes essential use of polynomials that are orthogonal with weight function f(sigma), which is taken here to be a Schulz distribution.