Modeling of fluid suspensions in deforming channels is a challenging problem namely due to the contact interactions between the particles and skeleton. We consider elastic skeletons of porous periodic structures saturated by fluid suspensions of rigid or deformable particles. Their diameter is comparable with the pore size so that the unilateral (frictionless) contact interaction must be treated to describe the flow and the particles transport through the porosity. The developed computational model is based on our recent results in modelling the self-contact interaction at the pore level of elastic porous media and modelling of the peristaltic deformation driven flows. In our setting, the particles are propulsed due to the interaction with the viscous pore-fluid flow and by the peristaltic deformation which is naturally caused by the fluid pulsations and the fluid-structure interaction (FSI). Asymptotic homogenization of the FSI problem is applied in the current reference configuration. At the microlevel, we consider locally periodic structures with only one particle in the reference periodic cell. The macroscopic model attains the form of a modified poroelasticity with deformation dependent effective poroelasticity coefficients of the Biot-Darcy continuum governing the macroscopic displacement and fluid pressure increments. The proposed computational homogenization algorithm for the contact fluid-structure interaction requires only a reduced number of resolved microstructures. To avoid exhaustive computations with deformed pore domains due to the contact, approximation schemes are employed using the sensitivity analysis are suggested which lead to reduced computational effort.