In this paper, we propose an online power allocation scheme to maximize the time averaged sum rate for multiple downlink receivers with energy harvesting transmitter. The transmitter employs non-orthogonal multiple access (NOMA) and/or orthogonal multiple access (OMA) to transmit data to multiple users. Additionally, we consider the scenario where each individual user has a quality of service constraint on its required instantaneous rate. The decisions of total transmit power and power allocation for different users in a given time slot are obtained with the help of Lyapunov optimization technique. The proposed schemes do not require any statistical information of the channel states and the harvested energy. The proposed power allocation schemes entail in small complexity based power allocation decisions. Therefore, the proposed schemes can provide solutions in real time and are more suited for online power allocation problems where the system state parameters (e.g. channel state, harvested energy etc) change quickly. The performances of the proposed schemes are demonstrated with the help of simulation results.