  In 1976, King defined certain tableaux model, called King tableaux in this
paper, counting weight multiplicities of irreducible representation of the
symplectic group $Sp(2m)$ for a given dominant weight. Since Kashiwara defined
crystals, it is an open problem to provide a crystal structure on King
tableaux. In this paper, we present crystal structures on King tableaux and
semistandard oscillating tableaux. The semistandard oscillating tableaux
naturally appear as $Q$-tableaux in the symplectic version of RSK algorithms.
As an application, we discuss Littlewood-Richardson coefficients for $Sp(2m)$
in terms of semistandard oscillating tableaux.
