An uplink multi secondary user (SU) cognitive radio system having average delay constraints as well as an interference constraint to the primary user (PU) is considered. If the interference channels between the SUs and the PU are statistically heterogeneous due to the different physical locations of the different SUs, the SUs will experience different delay performances. This is because SUs located closer to the PU transmit with lower power levels. Two dynamic scheduling-and-power-allocation policies that can provide the required average delay guarantees to all SUs irrespective of their locations are proposed. The first policy solves the problem when the interference constraint is an instantaneous one, while the second is for problems with long-term average interference constraints. We show that although the average interference problem is an extension to the instantaneous interference one, the solution is totally different. The two policies, derived using the Lyapunov optimization technique, are shown to be asymptotically delay optimal while satisfying the delay and interference constraints. Our findings are supported by extensive system simulations and shown to outperform existing policies as well as shown to be robust to channel estimation errors.