In this paper we study fair rate scheduling in an ad hoc cognitive wireless network with spectrum underlay. Transmissions in the network are allowed provided their interference to the primary network is below a predefined threshold. An optimal scheduling problem is formulated with an objective to achieve proportional fairness (PF) of the long-term average transmission rates among different links. Implementing the optimum scheduling requires high complexity. Two practical scheduling schemes are then proposed. In the first scheme, transmission priorities of the links are determined by their potential contributions to an objective utility function, assuming there is no co-channel interference within the network. In the second scheme, transmission priorities are derived from both the objective function and interference to the primary network. We also consider using exclusive regions to limit interference among simultaneous transmissions in order to improve the system throughput. The scheduling schemes can be implemented distributively in the ad hoc cognitive wireless network with limited assistance from the primary network. Our results show that the proposed PF scheduling schemes can achieve high overall throughput and close-to-optimum fairness, and using exclusive regions can improve the system utility without compromising the fairness performance.