To efficiently utilize nonexclusive underwater acoustic frequencies, we propose an Underwater Cooperative Spectrum Sharing (UCSS) protocol for a centralized underwater cognitive acoustic network that mainly consists of two parts. In the first part, to check the random occurrence of interferers periodically, the time domain is divided into frames that consist of a sensing and a non-sensing sub-frame. Then, we set the ratio of the two sub-frames to enhance the sensing rate via simulations. As a result, there exists the upper limit of the ratio, which can be used for determining the proportion of the sensing time within a frame. The second part is to design two heuristic resource allocation (RA) algorithms. One is a multiround RA (MRRA), where a central entity allocates a data channel (i.e., resource) to a CU each round so that multiple rounds are executed until no CUs need to be allocated or there is a lack of data channels. The other is a single-round RA (SRRA), where a CU is allocated to as many data channels as its QoS within a round. We also specify four rules to determine the allocation order of the CUs: random, fixed, high-QoS-based, and low-channel allocation-rate-based. In this study, we investigate the best RA allocation order pair supporting the highest channel allocation rate and fairness index via extensive simulations. It is shown that the MRRA outperformed the SRRA, regardless of allocation orders at any conditions, and the random and low-channel allocation-rate-based allocation orders with MRRA supported the best performance. In particular, even without the optimization process, the MRRA guarantees more than 95% fairness.