Many emerging multimedia streaming applications involve multiple users communicating under strict latency constraints. In this paper we study streaming codes for a network involving two source nodes, one relay node and a destination node. In our setting, each source node transmits a stream of messages, through the relay, to a destination, who is required to decode the messages under a strict delay constraint. For the case of a single source node, a class of streaming codes has been proposed by Fong et al. [2], using the concept of {\em delay-spectrum}. In the present work we present an in-depth analysis of the properties of delay-spectrum and apply them to develop streaming codes for our proposed setting through a novel framework. Our first scheme involves greedily selecting the rate on the link from relay to destination and using properties of the delay-spectrum to find feasible streaming codes that satisfy the required delay constraints. We provide a closed form expression for the achievable rate region and identify conditions when the proposed scheme is optimal by establishing a natural outer bound. Our second scheme builds upon this approach, but uses a numerical optimization-based approach to improve the achievable rate region over the first scheme. We demonstrate that our proposed schemes achieve significant improvements over baseline schemes based on single-user codes.