Investment on product greenness in green supply chain is always restricted by the emerging supplier’ financial constraints, so manufacturers always share the suppliers’ investment to encourage the suppliers’ green innovation. Based on the two-stage cooperation model between one manufacturer and one emerging supplier, and the assumption that emerging suppliers need to reach a certain survival threshold at the end of each period, this paper studies investment on product greenness and sustainability of cooperation in the supply chain. The impacts of consumers’ preference for greenness (CPG), market volatility, financial constraints, and investment-sharing proportion are also examined. It was found that when market volatility and CPG exist at the same time, compared with the deterministic environment, emerging suppliers will improve (or reduce) the wholesale price and greenness at the same time to balance the short-term bankruptcy risk and the long-term profit, and suppliers’ green investment would be stimulated by the increasing demand uncertainty. Besides, when suppliers’ financial constraints increase, manufacturers will also increase its sharing proportion of green investment. Lastly, there always exists an investment-sharing proportion that optimizes the sustainability of cooperation and profits jointly.