We have investigated the static second hyperpolarizabilities (γ) of the singlet diradical systems with intermediate diradical character involving phenalenyl radicals connected by acetylene and vinylene π-conjugated linkers, 1 and 2, using the hybrid density functional theory. For comparison, we have also examined the γ values of the closed-shell and pure diradical systems with almost the same molecular size as 1 and 2. In agreement with our previous prediction of the diradical character dependence of γ, it turns out that the γ values of 1 and 2 are significantly enhanced compared to those of the closed-shell and pure diradical systems. In the present case, distinct differences in y values are not observed between the two π-conjugated linkers, though the diradical character is found to depend on the kind of linker. Furthermore, we have investigated the spin multiplicity effect on γ. Changing from the singlet to the triplet state, the γ values of the systems with intermediate diradical character in the singlet state are quite reduced, though those of the pure diradical systems are hardly changed. Such spin multiplicity dependence of γ is understood by considering the difference of diradical character between their singlet states together with the Pauli principle. The present results provide a possibility of a novel control scheme of γ for phenalenyl radical systems involving π-conjugated linkers by adjusting the diradical character through the change of the linked position of π-conjugated linkers and the spin multiplicity.