  This article compares the Ks magnitude distribution of Small Magellanic Cloud
asymptotic giant branch stars obtained from the DENIS and 2MASS data with
theoretical distributions. Theoretical Ks magnitude distributions have been
constructed using up-to-date stellar evolution calculations for low and
intermediate-mass stars, and in particular for thermally pulsing asymptotic
giant branch stars. Separate fits of the magnitude distributions of carbon- and
oxygen-rich stars allowed us to constrain the metallicity distribution across
the galaxy and its star formation rate. The Small Magellanic Cloud stellar
population is found to be on average 7-9 Gyr old but older stars are present at
its periphery and younger stars are present in the direction of the companion
galaxy the Large Magellanic Cloud. The metallicity distribution traces a
ring-like structure that is more metal rich than the inner region of the
galaxy. The C/M ratio discussed in Paper I is a tracer of the metallicity
distribution only if the underlying stellar population is of intermediate-age.
