The intensity of surface-enhanced Raman scattering from cyanide adsorbed in air onto silver-island films is found to be highly nonlinear with coverage. We find it can be described by a classical calculation of microscopic local fields taking into account the electronic polarizabilities of nearby adsorbates. Absolute coverages and isotopic shifts are determined using $^{14}\mathrm{C}$ tracing. Our data are consistent with single CN groups adsorbed in two different types of on-top sites in the first monolayer on the silver islands only. Using a simple model, we calculate the classical electromagnetic enhancement of the CN stretching modes as a function of CN coverage, taking into account both macroscopic local fields and classical plasma resonances of the island film overcoated with a layer of adsorbates. We obtain excellent agreement both with the coverage dependence of the Raman scattering intensity and also of the shift in extinction of the island film itself, fitting both using one essential parameter, the electric polarizability of adsorbed CN. Our best-fit value for this parameter \ensuremath{\sim}5--6 A${\r{}}^{3}$ is in good agreement with the polarizability of gaseous HCN along the bond axis. We also directly compare our measured and calculated electromagnetic enhancements as a function of coverage to arrive at an estimate for the bonding-induced enhancement of 6\ifmmode\pm\else\textpm\fi{}3 for the adsorbed CN.