In this paper, cooperative resource allocation strategies are characterized for a spectrum-leasing based cognitive radio network (CRN), where the primary system leases the licensed band to the secondary system for a fraction of time in exchange for the secondary user (SU) acting as relay. Here, both amplify-and-forward (AF) and decode-and-forward (DF) relay protocols are considered. Considering the delay-sensitive traffic in CRN, the proposed strategies ensure delay provisioning for both primary user (PU) and SU with multiple system design objectives. In particular, we propose a multi-objective optimization framework, which incorporates two important system design objectives: the average sum power minimization and the leased time minimization. By integrating information theory with the concept of effective capacity, the adopted multi-objective optimization problem is recast as a convex optimization one via employing weighting method and sequentially solved by applying the Lagrangian dual method. It is shown that the global optimal solution of the original problem is characterized by a Pareto set which provides a quantitative insight into the tradeoff between the transmit power and leased time. Moreover, to learn the statistics of the wireless channels on the fly, we also put forward a stochastic iterative algorithm to achieve the optimal power and time allocation by employing the stochastic optimization theory. Numerical results not only reveal the nontrivial tradeoff among the considered conflicting system design objectives but also demonstrate that the proposed strategies perform better in saving wireless resources than existing resource allocation policies for different Quality-of-Service (QoS) exponent sets, especially when the delay requirement is strict.