The bulk piezoelectric response, as measured by the piezoelectric modulus tensor (textbf{d}), is determined by a combination of charge redistribution due to strain and the amount of strain produced by the application of stress (stiffness). Motivated by the notion that less stiff materials could exhibit large piezoelectric responses, herein we investigate the piezoelectric modulus of van der Waals-bonded quasi-2D ionic compounds using first-principles calculations. From a pool of 869 known binary and ternary quasi-2D materials, we have identified 135 non-centrosymmetric crystals of which 48 systems are found to have textbf{d} components larger than the longitudinal piezoelectric modulus of AlN (a common piezoelectric for resonators), and three systems with the response greater than that of PbTiO$_3$, which is among the materials with largest known piezoelectric modulus. None of the identified materials have previously been considered for piezoelectric applications. Furthermore, we find that large textbf{d} components always couple to the deformations (shearing or axial) of van der Waals gaps between the layers and are indeed enabled by the weak intra-layer interactions.
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