This work investigates adaptive random linear packet coding (RLPC) for reliable underwater acoustic (UWA) communications. Our goal is to minimize the total transmission time of data blocks by adjusting the packet coding rate. We first consider the application of RLPC with the conventional automatic repeat request (ARQ) scheme. We dynamically adjust the coding rate to fit the time variations of UWA channels by choosing the optimal number of packets in each transmission. The optimal number of packets in each transmission is obtained based on a dynamic programming (DP) algorithm according to the feedback messages, which contain the number of successfully transmitted packets in the last transmission and the channel state information. Furthermore, considering the long propagation delay of UWA communications, we propose a modified juggling-like ARQ (J-ARQ) for the RLPC scheme, for which the duration of each transmission can be adjusted based on the characteristics of RLPC. A two-step DP algorithm is proposed to find out the optimal solutions for this case. Simulation results show that the proposed schemes can improve the throughput efficiency and reduce the outage probability.