This paper addresses the problem of offering reliable causal multicast in a setting where nodes are organized in an overlay network and use this network to disseminate information among each other. The use of overlay networks for this purpose is widely used when the number of nodes is large. For instance, many publish-subscribe systems use an overlay of message brokers to support the exchange of information among publishers and subscribers. To the best of our knowledge, previous multicast algorithms for overlay networks either do not enforce causal order or, in order to do so, require nodes to keep metadata (for instance, sequence numbers) for all senders and are, therefore, inherently non-scalable. In this paper we propose a novel localized algorithm to implement reliable causal multicast, where each node is only required to keep metadata regarding nodes in its neighbourhood (with a radius that is a function of the number of faults that need to be tolerated). Experimental results show that our algorithm can achieve significant improvements over non-localized alternatives, and can even outperform localized algorithms that do not offer causal order.