For α decay half-life calculations in this work, the Coulomb and proximity potential model with a new semiempirical formula for diffuseness parameter developed in previous work [Phys. Rev. C 100, 024601 (2019)] is used. The present model in this work is compared with the generalized liquid-drop model (GLDM), universal decay law (UDL), and experimental half-lives in the region Z = 104 − 118. Next, the predicted half-lives of 51 superheavy nuclei (SHN) with Z = 122 − 125 by the present model are compared with those of GLDM, and UDL. The present model is revealed to be more accurate in reproducing experimental half-lives compared to GLDM and UDL. Moreover, it is found that the predictions of the present model and UDL are highly consistent while GLDM largely deviates from the other two. A study of the competition between α decay and spontaneous fission (SF) shows that α decay is the dominant mode. Among the studied SHN with Z = 122−125, 295−307 122 and 314−320 125 are identified as potential candidates whose half-lives are relatively long enough to be experimentally detected in the future through their α-decay chains. The identified candidates are in good agreement with other recent work.