  The interplay between steering and quantum coherence is studied in a
scenario, where two atoms move through an external massless scalar field. We
show that just like entanglement, the steering induced coherence of the
equilibrium state may increase or decrease with acceleration depending on the
initial condition of the state. We also investigate the condition for coherence
steerability - as opposed to simple state steerability. Interestingly, we find
that the quantum coherence of the equilibrium state cannot be steered, even
when the steering induced coherence is non-zero. We argue that under any
condition, gravity prohibits the coherence steering of the equilibrium state.
