We consider a cognitive radio network with one primary (PU), one secondary user (SU), and two distinct destinations. SU not only exploits the idle time slots (i.e. PU is not transmitting) to send its own packets, but also interfere with the PU with a certain probability that is optimized to maximize the stable throughput of the SU under a delay constraint for the PU. This optimization problem is formulated using two schemes. First, the hard delay guarantee scheme where the objective is to maximize the throughput of the SU subject to the delay of the PU's packet is less than a certain value. Second, the soft delay guarantee scheme where the objective is to minimize the delay of the PU's packets minus a constant multiplied by the throughput of the SU. Numerical results reveal that none of the proposed outperforms the other in general. The first scheme ensures a fix delay performance for the PU's packets on the boundary of the stability region. While the second scheme guarantees a finite delay performance with higher stable throughput than that of the first scheme.