In this paper, we develop a distributed stochastic learning framework for seeking Nash equilibria under state dependent payoff functions. Most of the existing works assumes that a closed form expression of the reward is available at the nodes. We consider here a realistic assumption that the nodes have only a numerical realization of the reward at each time and develop a discrete time stochastic learning using sinus perturbation. We examine the convergence of our discrete time algorithm to a limiting trajectory defined by an Ordinary Differential Equation (ODE). Finally, we conduct a stability analysis and apply the proposed scheme in a generic power control problem in wireless networks.