In this paper, we consider coexistence of secondary and primary users who share particular portions of the spectrum and propose a delay-constrained power and rate allocation scheme for the secondary user link. Secondary users are allowed to access the spectrum occupied by a primary user subject to satisfying interference-power limitations imposed by the primary user. Applying this limitation, we obtain the maximum arrival-rate supported by the secondary channel in Nakagami-m block-fading environment subject to satisfying a given statistical delay quality-of-service (QoS) constraint. In this respect, we derive the optimal rate and power adaptation policy that maximizes the effective capacity of the channel, and provide closed-form expressions for the power allocation and the effective capacity. In addition, we obtain closed-form expressions for the expenditure-power that is required at the secondary transmitter to achieve the above-mentioned capacity metric. Moreover, for comparison purposes, we consider two widely deployed power allocation strategies, namely, optimal power and rate allocation (opra) and channel inversion with fixed rate (cifr), and investigate the effective capacity of the channel under these power transmission techniques. Numerical simulations are conducted to corroborate our theoretical results.