We analyze stability of self-enforcing climate agreements based on a data set generated by the CLIMNEG world simulation model (CWSM), version 1.2. We consider two new aspects which appear important in actual treaty-making. First, we consider a sequential coalition formation process where players can make proposals which are either accepted or countered by other proposals. Second, we analyze whether a moderator, like an international organization, even without enforcement power, can improve upon globally suboptimal outcomes through coordinating actions by making recommendations that must be Pareto-improving to all parties. We discuss the conceptual difficulties of implementing our algorithm.