We explore the possibility of engineering quantum states of a charged mechanical oscillator by coupling it to a stream of atoms in superpositions of high-lying Rydberg states. Our scheme relies on the driving of a two-phonon resonance within the oscillator by coupling it to an atomic two-photon transition. This approach effectuates a controllable open system dynamics on the oscillator that in principle permits versatile dissipative creation of squeezed and other nonclassical states which are central to sensing applications or for studies of fundamental questions concerning the boundary between classical and quantum-mechanical descriptions of macroscopic objects. We show that these features survive thermal coupling of the oscillator with the environment. We perform a detailed feasibility study finding that current state-of-the-art parameters result in atom-oscillator couplings which are too weak to efficiently implement the proposed oscillator state preparation protocol. Finally, we comment on ways to circumvent the present limitations.