We assess the ionizing effect of low-energy protostellar cosmic rays in protoplanetary discs around a young solar mass star for a wide range of disc parameters. We assume a source of low-energy cosmic rays located close to the young star that travels diffusively through the protoplanetary disc. We use observationally inferred values from nearby star-forming regions for the total disc mass and the radial density profile. We investigate the influence of varying the disc mass within the observed scatter for a solar mass star. We find that for a large range of disc masses and density profiles that protoplanetary discs are 'optically thin' to low-energy (similar to 3GeV) cosmic rays. At R similar to 10 au, for all of the discs that we consider (M-disc = 6.0 x 10(-4)-2.4 x 10(-2) M-circle dot), the ionization rate due to low-energy stellar cosmic rays is larger than that expected from unmodulated galactic cosmic rays. This is in contrast to our previous results that assumed a much denser disc that may be appropriate for a more embedded source. At R similar to 70 au, the ionization rate due to stellar cosmic rays dominates in similar to 50 per cent of the discs. These are the less massive discs with less steep density profiles. At this radius, there is at least an order of magnitude difference in the ionization rate between the least and most massive disc that we consider. Our results indicate, for a wide range of disc masses, that low-energy stellar cosmic rays provide an important source of ionization at the disc mid-plane at large radii (similar to 70 au).