Magnetocaloric effect in cryogenic temperature regime has gained enormous attention due to its application in the field of cryogenic refrigeration technology, which is required for quantum computing, space sciences and basic research activities. In this context, Gd and Dy based frustrated systems are considered as promising cryogenic magnetocaloric materials. Hence, magnetic and magnetocaloric properties of GdTaO4, GdNbO4 and DyNbO4 are comprehensively investigated. Structural analysis suggest that these compounds crystallize in monoclinic structure, wherein magnetic ions form an elongated diamond geometry. The analysis of magnetization, heat capacity and field dependent magnetic entropy change confirm the presence of short-range magnetic correlations in these compounds. Additionally, a remarkably large magnetic entropy change, and relative cooling power are noted. The mechanical efficiency is found comparable (or even better) to those reported for good magnetic refrigerants. Our study suggests that GdTaO4, GdNbO4 and DyNbO4 can be regarded as promising cryogenic magnetic refrigerant materials.