ABSTRACT X-ray polarimetry missions like Imaging X-ray Polarimetry Explorer will be able to measure for the first time the polarization properties of accreting, weakly magnetized neutron stars in low-mass X-ray binaries. In this work, we present simulations of the expected X-ray polarized signal, including the coronal emission for different geometries of the corona itself, i.e. a slab above the accretion disc and a spherical shell around the neutron star. The simulations are performed with the fully relativistic Monte Carlo code monk capable of computing the X-ray polarization degree and angle for various physical input parameters of the neutron star, disc, and corona. Different coronal geometries result in significantly different X-ray polarization properties, which can therefore be used to constrain the geometry of the systems.