We analyse agreements on river water allocation between riparian countries. Besides being efficient, water allocation agreements need to be stable in order to be effective in increasing the efficiency of water use. In this paper, we assess the stability of water allocation agreements, using a game theoretic model. We consider the effects of climate change and the choice of a sharing rule on stability. Our results show that both a decrease in mean river flow and an increase in the variance of river flow decrease the stability of an agreement. An agreement where the downstream country is allocated a fixed amount of water has the lowest stability compared to other sharing rules.