Computational design can accelerate the discovery of new materials with tailored properties, but applying this approach to plasmonic nanoparticles with diameters larger than a few nanometers is challenging as atomistic first-principles calculations are not feasible for such systems. In this paper, we employ a recently developed material-specific approach that combines effective mass theory for electrons with a quasistatic description of the localized surface plasmon to identify promising bimetallic core-shell nanoparticles for hot-electron photocatalysis. Specifically, we calculate hot-carrier generation rates of 100 different core-shell nanoparticles and find that systems with an alkali-metal core and a transition-metal shell exhibit high figures of merit for water splitting and are stable in aqueous environments. Our analysis reveals that the high efficiency of these systems is related to their electronic structure, which features a two-dimensional electron gas in the shell. Our calculations further demonstrate that hot-carrier properties are highly tunable and depend sensitively on core and shell sizes. The design rules resulting from our work can guide experimental progress towards improved solar energy conversion devices.