In this paper, we have calculated parity nonconserving electric dipole amplitudes of the hyperfine components for the transitions between the ground and first excited states of ${}^{137}{\mathrm{Ba}}^{+}$ and ${}^{87}{\mathrm{Sr}}^{+}$ using sum-over-states technique. The results are presented to extract the constants associated with the nuclear spin-dependent amplitudes from experimental measurements. The wave functions to calculate the most dominant part of the sums are constructed using highly correlated coupled-cluster theory based on the Dirac-Coulomb-Gaunt Hamiltonian.