We consider the problem of multi-user spectrum access in wireless networks. The bandwidth is divided into K orthogonal channels, and M users aim to access the spectrum. Each user chooses a single channel for transmission at each time slot. The state of each channel is modeled by a restless unknown Markovian process. Previous studies have analyzed a special case of this setting, in which each channel yields the same expected rate for all users. By contrast, we consider a more general and practical model, where each channel yields a different expected rate for each user. This model adds a significant challenge of how to efficiently learn a channel allocation in a distributed manner to yield a global system-wide objective. We adopt the stable matching utility as the system objective, which is known to yield strong performance in multichannel wireless networks, and develop a novel Distributed Stable Strategy Learning (DSSL) algorithm to achieve the objective. We prove theoretically that DSSL converges to the stable matching allocation, and the regret, defined as the loss in total rate with respect to the stable matching solution, has a logarithmic order with time. Finally, simulation results demonstrate the strong performance of the DSSL algorithm.