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.
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