ESA's Hera mission is planning to land a probe on the surface of the secondary body of the Didymos binary asteroid system, called Dimorphos, using a ballistic landing strategy. Ballistic landings can be sensitive to uncertainties in the deployment of the lander and the environment models. Thus, the design of the ballistic landing trajectory needs to take into consideration both the minimization of the touchdown velocity and the robustness of the trajectory against uncertainties. In this research, a landing trajectory design algorithm that accomplishes both these tasks is developed. This is done using the Generalised Intrusive Polynomial Algebra (GIPA) method to propagate the uncertainties through the dynamical system. A novel addition to GIPA is introduced, which is able to obtain the probability distribution of the spacecraft state over time. The landing trajectory design method is tested using several different landing area sizes and locations. It is found that there is a large difference between the found minimal touchdown velocities between landing locations. Furthermore, a larger allowed landing area results in more deployment states being allowed, at the expense of higher touchdown velocities. The algorithm developed here thus allows for the design of robust ballistic landing trajectories for landing on small bodies like Dimorphos.