Energy harvesting is an emerging technology providing clean energy for wireless communication systems. Due to the randomness in energy arrivals, wireless service process needs to be matched with energy provision to avoid energy waste or shortage. Other than passively adjusting energy usage according to traffic and energy profiles, a framework, namely, GreenDelivery has been proposed to proactively push popular contents to users in advance, such that harvested energy can be utilized more efficiently. In this paper, a heterogeneous network with multiple GreenDelivery small cells is considered. Due to spatial proximity, adjacent small cells might conflict with each other due to simultaneous transmissions or repeated pushes of identical contents to the same user, which calls for a more sophisticated design of push scheme in a multi-cell scenario. To tackle the interference, small base station (SBS) scheduling is proposed, exploiting the intermittent nature of renewable energy, to temporally separate the transmission of adjacent small cells. Heuristic push schemes are then proposed to further reduce the user requests handled by macro base stations (MBS) with centralized and distributed realizations. Simulations show that the proposed push schemes outperform the baseline scheme in which contents are pushed in the descending order of their popularities, especially when content popularity is more uniformly distributed.