During the drying of drops of nanoparticle suspensions, segregation can occur by internal fluid flows toward the contact line, if the contact line is pinned. This leads to a characteristic ring deposit or coffee stain. On solid substrates coffee staining can be eliminated through the use of solvent mixtures that promote Marangoni flows to oppose these drying-induced flows. Here it is shown that a suspension, optimized to eliminate the formation of coffee stains on a range of solid surfaces, shows coffee staining on a number of porous surfaces. This behavior is shown to be consistent with a mechanism of fluid removal through capillary flow (draining) of the solvent into the porous substrate, combined with filtration of the particles by the small pore size, in addition to the flow from solvent evaporation. The extent of capillary driven coffee staining is a function of substrate pore size: if the pore size is small, capillary flow is slow, reducing the observed coffee staining. However, if the pore size is too large, the nanoparticles are absorbed into the material along with the draining solute and no deposition of particles is observed.