  This paper is Part II of a two-part series on coexistence states study in
stochastic generalized Kolmogorov systems under small diffusion. Part I
provided a complete characterization for approximating invariant probability
measures and density functions, while here, we focus on explicit approximations
for periodic solutions in distribution. Two easily implementable methods are
introduced: periodic normal approximation (PNOA) and periodic log-normal
approximation (PLNA). These methods offer unified algorithms to calculate the
mean and covariance matrix, and verify positive definiteness, without
additional constraints like non-degenerate diffusion. Furthermore, we explore
essential properties of the covariance matrix, particularly its connection
under periodic and non-periodic drift coefficients. Our new approximation
methods significantly relax the minimal criteria for positive definiteness of
the solution of the discrete-type Lyapunov equation. Some numerical experiments
are provided to support our theoretical results.
