Gravitational well is a widely used system for the verification of the quantum weak equivalence principle (WEP). We have studied the quantum gravitational well (GW) under the shed of non-commutative (NC) space so that the results can be utilized for testing the validity of WEP in NC-space. To keep our study widely usable, we have considered both position-position and momentum-momentum non-commutativity. Since coherent state (CS) structure provides a natural bridge between the classical and quantum domain descriptions, the quantum domain validity of purely classical phenomena like free-fall under gravity might be verified with the help of CS. We have constructed CS with the aid of a Lewis-Riesenfeld phase space invariant operator. We deduced the uncertainty relations from the expectation values of the observables and shown that the solutions of the time-dependent Schrödinger equation are squeezed-coherent states.

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