Coalition loyalty programmes (CLPs) are owned and operated as for-profit enterprises. We consider the ordering decisions of rewards that arise in this context, under a general setting in which not only is the demand for rewards uncertain, but also the CLP firm offers bonus points, a very common cooperative promotion mechanism used in loyalty programmes. The rewards are acquired either at a wholesale ‘discounted’ cost or at a wholesale ‘non-discounted’ cost by the CLP firm from its multiple commercial partners and supplied to customers seeking to redeem their accumulated ‘reward points’, subject to commercial partners’ capacities for offering rewards, the firm’s overall budget for purchasing rewards, and its control policy on points liability. We formulate the problem as a stochastic linear programme with recourse and solve it using a sampling-based heuristic solution procedure previously discussed in the literature. We report on the managerial applicability of our model in dealing with the redemption budget spending resulting from changes in demand variability, changes in the redemption budget, and the control of liability levels within a reasonable range.