The protocols in underwater acoustic wireless sensor networks (UAWSNs) that address reliability in packets forwarding usually consider the connectivity of the routing paths up to one- or two-hops. Since senor nodes are connected with one another using other nodes in their neighborhood, such protocols have compromised reliability. It is because these protocols do not guarantee the presence of neighbors beyond the selected one- or two-hops for connectivity and path establishment. This is further worsened by the harshness and unpredictability of the underwater scenario. In addition, establishment of the routing paths usually requires the nodes’ undersea geographical locations, which is infeasible because currents in water cause the nodes to move from one position to another. To overcome these challenges, this paper presents two routing schemes for UAWSNs: reliability-aware routing (RAR) and reliability-aware cooperative routing with adaptive amplification (RACAA). RAR considers complete path connectivity to advance packets to sea surface. This overcomes packets loss when connectivity is not established and forwarder nodes are not available for data routing. For all the established paths, the probability of successfully transmitting data packets is calculated. This avoids the adverse channel effects. However, sea channel is unpredictable and fluctuating and its properties may change after its computation and prior to information transmission. Therefore, cooperative routing is introduced to RAR with adaptive power control of relays, which makes the RACCA protocol. In RACAA, a relay node increases its transmit power than normal when the error in the data; it receives from the sender, is more than 50 % before transferring it further to destination. This further increases the reliability when such packets are forwarded. Unlike the conventional approach, the proposed protocols are independent of knowing the geographical locations of nodes in establishing the routes, which is computationally challenging due to nodes’ movements with ocean currents and tides. Simulation results exhibit that RAR and RACAA outperform the counterpart scheme in delivering packets to the water surface.