Energy harvesting (EH) has recently emerged as a promising technology for next-generation green wireless networks, as it can power communication nodes with renewable energy. However, it is challenging to provide satisfactory performance in such systems, due to the sporadic energy arrival and the low harvesting rate. In this paper, we propose a novel cooperation strategy for EH networks with the help of multiple EH relays, each of a steady but low harvesting rate. Different relays will take turns to assist the source-destination transmission, and thus energy diversity can be achieved. To provide steady communications, we formulate the design problem as to maximize the minimum utility during the considered transmission duration, which, however, is NP-hard. We propose a general framework to develop efficient suboptimal algorithms, which consists of 1) a sufficient condition for the feasibility of the optimization problem and 2) an efficient bisection algorithm to find a suboptimal solution. Simulation results will show that the proposed cooperation strategy can provide significant power gains over the direct link transmission, and the proposed suboptimal algorithm can provide near-optimal performance. Compared to the best-effort cooperation that only optimizes the current transmission block, the proposed strategy can achieve the same performance with much fewer relays.