This article is the second of two papers (for Part I, see [ibid. 217, No. 10, 1807–1824 (2013; Zbl 1301.22008)]) on the pairs of complex classical groups \[ (G,K) = (\mathrm{Sp}\;\!(2n),\mathrm{Sp}\;\!(2p)\times \mathrm{Sp}\;\!(2q)) \quad \text{and} \quad (G,K) = (\mathrm{SO}(2n),\mathrm{GL}(n)), \] where \(p + q = n\), which fall, respectively, in the two cases referred to as type C and type D and have the real forms \(G_\mathbf{R} = \mathrm{Sp}\,(p,q)\,\text{and}\, G_\mathbf{R} = \mathrm{SO}^*(2n)\). Two previous papers by the same authors, in collaboration with W. Graham for the second one, were devoted to other pairs [J. Algebra 345, No. 1, 109–136 (2011; Zbl 1254.22007); J. Algebra 345, No. 1, 100–108 (2011; Zbl 1253.22009)] and here we use the notation and terminology of the review of the first one. In Part I of this paper on the pairs \((G,K)\) quoted above [L. Barchini and R. Zierau, J. Pure Appl. Algebra 217, No. 10, 1807–1824 (2013; Zbl 1301.22008)], the authors first gave an algorithm to determine an element \(f\) of a Borel subalgebra \(\mathfrak b = \mathfrak h + \mathfrak n^-\) of \(\mathfrak g = \mathfrak k + \mathfrak p\) generic in \(\mathfrak n^-\cap\mathfrak p\), thence to compute \(\overline{K\cdot f} = \gamma_{\mathcal Q}(T^*_{\mathcal Q}\mathcal B)\) from the closed \(K\)-orbit \(\mathcal Q = K\cdot\mathfrak b\) in the flag variety \(\mathcal B\) of \(G\), and then a description of \(\gamma_{\mathcal Q}^{-1}(f)\), the Springer fiber over \(f\) associated to \(\mathcal Q\). This second article provides a method to calculate associated cycles of irreducible discrete series representations of \(G_\mathbf{R}\). Let \(X\) be an irreducible discrete series representation of \(G_\mathbf{R}\) with trivial infinitesimal character \(\rho\) and associated to a closed \(K\)-orbit \(\mathcal Q\) in \(\mathcal B\) by the Beilinson-Bernstein localization theory of Harish-Chandra modules [A. Beilinson and J. Bernstein, C. R. Acad. Sci., Paris, Sér. I 292, 15–18 (1981; Zbl 0476.14019)]. There is a coherent family \((X_\lambda)_{\lambda\in\Lambda}\) with \(X_\rho = X\), where \(\Lambda\) is the integral lattice in \(\mathfrak h^*\), and the associated cycle of \(X_\lambda \, (\lambda\in\Lambda^+)\) is \(m_{\mathcal Q}(\lambda)\overline{K\cdot f}\). By a result of J.-T. Chang [Trans. Am. Math. Soc. 334, No. 1, 213–227 (1992; Zbl 0785.22016)], the multiplicity polynomial \(m_{\mathcal Q}(\lambda)\) is the dimension of a \(0^{\text{th}}\)-cohomology space of \(\gamma_{\mathcal Q}^{-1}(f)\) with coefficients in the restriction to \(\gamma_{\mathcal Q}^{-1}(f)\) of a sheaf of sections and is sometimes directly computable. However, for the real forms \(G_\mathbf{R}\) considered in the present paper, \(\gamma_{\mathcal Q}^{-1}(f)\) does not have a suitable form for every closed \(K\)-orbit \(\mathcal Q\) and so the authors apply another algorithm. Instead of \(f\), they choose a “nice” generic element \(f'\) and replace \(\mathcal Q\) by a closed \(K\)-orbit \(\mathcal Q'\) in \(\mathcal B\) for which \(\gamma_{\mathcal Q'}^{-1}(f')\) has a very simple form. The irreducible discrete series representation \(X'\) of \(G_\mathbf{R}\) with trivial infinitesimal character \(\rho\) and associated to \(\mathcal Q'\) is in the same Harish-Chandra cell as \(X\) and there is a coherent family \((X'_\lambda)_{\lambda\in\Lambda}\) so that \(X'_\rho = X'\). The multiplicity polynomial \(m_{\mathcal Q'}(\lambda) \, (\lambda\in\Lambda^+)\) can now be easily computed by the Borel-Weil Theorem and the Weyl Dimension Formula in type D, with a bit more of difficulty in type C, and then used to derive \(m_{\mathcal Q}(\lambda)\).