We have studied the ortho, para, and, in the case of D₃⁺, meta forms of the multiply-deuterated isotopes of H₃⁺, under physical conditions believed to be appropriate to pre-protostellar cores. As deuterons have integral nuclear spin, I = 1, Bose-Einstein statistical laws apply. Having extended the network of chemical reactions used in our previous study (Walmsley et al. \cite{walmsley04}), we have calculated the population densities of ortho- and para-D₂H⁺ and of ortho- and meta-D₃⁺. In the former case, comparison is made with the recent observations of para-D₂H⁺ in the prestellar core 16293E (Vastel et al. \cite{vastel04}). Using radiative transition probabilities computed by Ramanlal & Tennyson (\cite{ramanlal04}), we have predicted the intensities of the near infrared vibrational transitions of the deuterated isotopes of H₃⁺. Many of these transitions can be observed, in absorption, only from above the Earth's atmosphere, but some might be detectable through atmospheric windows.