Using the extended discrete interaction model we investigate the tunabilty of surface plasmon resonances in alloys and core-shell nanoparticles made from silver and gold in the small (1-15 nm) nanoscale regime where classical models based on the bulk dielectric constant may not apply. We show that the surface plasmon resonance of these alloys and core-shell particles to a large extent follow Vegard's law irrespective of the geometry of the nanoparticle. The evolution of the polarizability with size demonstrates a highly non-linear behaviour of the polarizability with the ratio of the constituents and geometry in alloys and core-shell nanoparticles, with the exception of the longitudinal surface plasmon resonance in nanorods and, partly, nanodisc alloys. We here show that the non-linear behaviour can be explained in terms of the difference in polarizability of the mixing constituents and local effects causing a quenching of the dipoles for geometries with a low aspect ratio. A thorough statistical investigation reveals that there is only a small dependence of the surface plasmon resonance on atomic arrangement and exact distribution in a nanoparticle and that the standard deviation decreases rapidly with the size of the nanoparticles. The physical ground for the random distribution algorithm for alloys in discrete interaction models is explained in detail and verified by a statistical analysis. For nanoparticles below 4 nm a sampling strategy is recommended.