In this paper, the problem of joint relay selection and max‐min energy‐efficient power allocation (J‐RS‐MMEE‐PA) in downlink multicell nonorthogonal multiple access (NOMA) networks is studied. In particular, the goal is to perform relay selection for each cellular user within each cell, so as to achieve max‐min energy efficiency while satisfying quality‐of‐service (QoS) constraints. However, the formulated J‐RS‐MMEE‐PA problem happens to be nonconvex (ie, computationally intensive). In turn, a solution procedure for max‐min energy‐efficient power allocation is devised to determine the energy efficiency of each user per potential relay while meeting the target minimum rate per user. After that, the relay selection problem is modeled as a student‐project allocation with preferences over projects matching problem. A polynomial‐time complexity stable matching (SM) algorithm is proposed, which takes into account the maximum number of users that can select a relay as well as the number of users that can be associated with a base station. However, the proposed SM algorithm can only guarantee an SM size that is at least half the size of the maximum “optimal” cardinality SM. Thus, the improved SM (I‐SM) algorithm with polynomial‐time complexity is devised, so as to guarantee an SM size that is at least two‐thirds of that of the optimal matching. Lastly, simulation results are presented to compare the proposed matching algorithms to the J‐RS‐MMEE‐PA scheme, where it has been shown that the I‐SM algorithm is superior to its SM counterpart and yields comparable energy efficiency per cellular user to the J‐RS‐MMEE‐PA scheme while satisfying QoS constraints.