Optically heterodyne-detected optical Kerr effect experiments are applied to study the orientational dynamics of the supercooled ionic organic liquids N-propyl-3-methylpyridinium bis( trifluoromethylsulfonyl) imide (PMPIm) and 1-ethyl-3-methylimidazolium tosylate (EMImTOS). The orientational dynamics are complex with relaxation involving several power law decays followed by a final exponential decay. A mode coupling theory (MCT) schematic model, the Sjogren model, was able to reproduce the PMPIm data very successfully over a wide range of times from 1 ps to hundreds of ns for all temperatures studied. Over the temperature range from room temperature down to the critical temperature T-c of 231 K, the OHD-OKE signal of PMPIm is characterized by the intermediate power law t(-1.00 +/- 0.04) at short times, a von Schweidler power law t(-0.51 +/- 0.03) at intermediate times, and a highly temperature-dependent exponential ( alpha relaxation) at long times. This form of the decay is identical to the form observed previously for a large number of organic van der Waals liquids. MCT analysis indicates that the theory can explain the experimental data very well for a range of temperatures above T-c, but as might be expected, there are some deviations from the theoretical modeling at temperatures close to T-c. For EMImTOS, the orientational dynamics were studied on the ps time scale in the deeply supercooled region near its glass transition temperature. The orientational relaxation of EMImTOS clearly displays the feature associated with the boson peak at similar to 2 ps, which is the first time domain evidence of the boson peak in ionic organic liquids. Overall, all the dynamical features observed earlier for organic van der Waals liquids using the same experimental technique are also observed for organic ionic liquids.