The network charge of polyampholyte microgels can be tuned by varying the pH of the surrounding solution, and a charge reversal from a positively charged microgel at low pH to a negatively charged microgel at high pH can be achieved. In a titration experiment, it is difficult to tell apart the ionisation of the acidic and basic monomers in the network and to determine the distribution of charges in the network, whereas using Metropolis Monte Carlo simulations, both the degree of ionisation and the distribution of ionised monomers can be determined separately for both species. Building on our earlier work on alternating polyampholyte microgels, we now investigated the pH-dependent ionisation and the swelling behaviour of polyampholyte core-shell microgels under good solvent conditions. For this purpose, we performed Metropolis Monte Carlo simulations for a bead-spring model using the constant-pH method. As in our previous study on alternating microgels, the width of the U-shaped curve of the microgels volume as a function of pH depends on the relative dissociation constants of acid and base, and the microgel volume can be approximated by a linear function of the total network charge. Due to the spatial separation of acid and base in core-shell systems, the ionisation is less enhanced compared to a microgel with an alternating distribution of the two species. Nevertheless, we still see an influence of the presence of one species on the ionisation behaviour of the other species under good solvent conditions. Furthermore, the isoelectric point is shifted towards higher pH, which is caused by a higher charge density in the core compared to that in the shell. Added salt changes the Donnan equilibrium, which determines the counterion distribution within and outside of the microgel. At the same time, it contributes to the electrostatic screening of the network charges, leading to a narrowing of the U-shaped volume transition curve.