In our previous work [Phys. Rev. D 101 (2020) 075046], we have proposed to install FAr Detectors at the Electron Positron Collider (FADEPC) to enhance the discovery potential of the long-lived particles (LLPs). In this study, we consider eight designs of far detectors with different locations, volumes and geometries and investigate their potential for discovering long-lived axion-like particles (ALPs) via the process e − e + → γ a, a → γγ at future e − e + colliders running at center-of-mass energy of √ s = 91.2 GeV and integrated luminosities of 16, 150, and 750 ab −1 . We estimate their sensitivities on the model parameters in terms of the effective ALP-photon-photon coupling Cγγ/Λ, the effective ALP-photon-Z coupling CγZ /Λ, and ALP mass ma for three physics scenarios: CγZ = 0; CγZ = Cγγ and both CγZ and Cγγ can freely change.