By using a two-dimensional Fourier representation of the Green tensor for Stokes flow between parallel walls, we calculate all friction and mobility functions for a single spherical particle moving between two walls subject to Poiseuille flow. The method readily generalises to N particles. For a channel narrow with respect to particle size, superposition of one-wall results is not an accurate approximation for the two-wall problem. Translation-rotation coupling is significant and changes its sign as the lateral position of the particle ranges across the channel. We illustrate these two-wall effects by calculating the trajectories of a magnetic colloid particle in Poiseuille flow subject to an external magnetic field.