Derivation of a Fourier-Chebyshev discretization of Stokes equations for doubly-periodic geometries with a bottom wall or a slit channel. No slip BCs are prescribed at the walls. The ultimate goal is to obtain velocities of externally forced particles suspended in the fluid, and to that end, I use the force-coupling method. The prototype MATLAB codes are currently maintained in our group's private repository, but can be provided if requested by email at srn324@nyu.edu.