This paper considers an opportunistic scheduling problem over a renewal system. A controller observes a random event at the beginning of each renewal frame and then chooses an action in response to the event, which affects the duration of the frame, the amount of resources used, and a penalty metric. The goal is to make frame-wise decisions so as to minimize the time average penalty subject to time average resource constraints. This problem has applications to task processing and communication in data networks, as well as to certain classes of Markov decision problems. We formulate the problem as a dynamic fractional program and propose an adaptive algorithm which uses an empirical accumulation as a feedback parameter. A key feature of the proposed algorithm is that it does not require knowledge of the random event statistics and potentially allows (uncountably) infinite event sets. We prove the algorithm satisfies all desired constraints and achieves $O(ε)$ near optimality with probability 1.