Charge qubits can be created and manipulated in solid-state double-quantum-dot (DQD) platforms. Typically, these systems are strongly affected by quantum noise stemming from coupling to substrate phonons. This is usually assumed to lead to decoherence towards steady states that are diagonal in the energy eigenbasis. In this letter we show, to the contrary, that due to the presence of phonons the equilibrium steady state of the DQD charge qubit may be engineered to display coherence in the energy eigenbasis. The magnitude of the coherence can be controlled by tuning the DQD parameters and regimes of high purity maybe found. In addition, we show that the steady-state coherence can be used to drive an auxiliary cavity mode coupled to the DQD. arXiv:1906.06271v1 [cond-mat.mes-hall]