  Deuterated interstellar molecules frequently have abundances relative to
their main isotopologues much higher than the overall elemental D-to-H ratio in
the cold dense interstellar medium. The H$_3^+$ and its isotopologues play a
key role in the deuterium fractionation; however, the abundances of these
isotopologues have not been measured empirically with respect to H$_3^+$ to
date. Our aim was to constrain the relative abundances of H$_2$D$^+$ and
D$_3^+$ in the cold outer envelope of the hot core CRL 2136 IRS 1. We carried
out three observations targeting H$_3^+$ and its isotopologues using the
spectrographs CRIRES at the VLT, iSHELL at IRTF, and EXES on board SOFIA. In
addition, the CO overtone band at 2.3 $\mu$m was observed by iSHELL to
characterize the gas on the line of sight. The H$_3^+$ ion was detected toward
CRL 2136 IRS 1 as in previous observations. Spectroscopy of lines of H$_2$D$^+$
and D$_3^+$ resulted in non-detections. The 3$\sigma$ upper limits of $N({\rm
H_2D^+})/N({\rm H_3^+})$ and $N({\rm D_3^+})/N({\rm H_3^+})$ are 0.24 and 0.13,
respectively. The population diagram for CO is reproduced by two components of
warm gas with the temperatures 58 K and 530 K, assuming a local thermodynamic
equilibrium (LTE) distribution of the rotational levels. Cold gas ($<$20 K)
makes only a minor contribution to the CO molecular column toward CRL 2136 IRS
1. The critical conditions for deuterium fractionation in a dense cloud are low
temperature and CO depletion. Given the revised cloud properties, it is no
surprise that H$_3^+$ isotopologues are not detected toward CRL 2136 IRS 1. The
result is consistent with our current understanding of how deuterium
fractionation proceeds.
