In this paper, we investigate effective capacity by modeling a cognitive radio broadcast channel with one secondary transmitter (ST) and two secondary receivers (SRs) under quality-of-service constraints and interference power limitations. We initially describe three different cooperative channel sensing strategies with different hard-decision combining algorithms at the ST, namely OR, Majority, and AND rules. Since the channel sensing occurs with possible errors, we consider a combined interference power constraint by which the transmission power of the secondary users (SUs) is bounded when the channel is sensed as both busy and idle. Furthermore, regarding the channel sensing decision and its correctness, there exist possibly four different transmission scenarios. We provide the instantaneous ergodic capacities of the channel between the ST and each SR in all of these scenarios. Granting that transmission outage arises when the instantaneous transmission rate is greater than the instantaneous ergodic capacity, we establish two different transmission rate policies for the SUs when the channel is sensed as idle. One of these policies features a greedy approach disregarding a possible transmission outage, and the other favors a precautious manner to prevent this outage. Subsequently, we determine the effective capacity region of this channel model, and we attain the power allocation policies that maximize this region. Finally, we present the numerical results. We first show the superiority of Majority rule when the channel sensing results are good. Then, we illustrate that a greedy transmission rate approach is more beneficial for the SUs under strict interference power constraints, whereas sending with lower rates will be more advantageous under loose interference constraints.