We present a hardware mechanism called HourGlass to predictably share data in a multi-core system where cores are explicitly designated as critical or non-critical. HourGlass is a time-based cache coherence protocol for dual-critical multi-core systems that ensures worst-case latency (WCL) bounds for memory requests originating from critical cores. Although HourGlass does not provide either WCL or bandwidth guarantees for memory requests from non-critical cores, it promotes the use of timers to improve its bandwidth utilization while still maintaining WCL bounds for critical cores. This encourages a trade-off between the WCL bounds for critical cores, and the improved memory bandwidth for non-critical cores via timer configurations. We evaluate HourGlass using gem5, and with multithreaded benchmark suites including SPLASH-2, and synthetic workloads. Our results show that the WCL for critical cores with HourGlass is always within the analytical WCL bounds, and provides a tighter WCL bound on critical cores compared to the state-of-the-art real-time cache coherence protocol. Further, we show that HourGlass enables a trade-off between provable WCL bounds for critical cores, and improved bandwidth utilization for non-critical cores. The average-case performance of HourGlass is comparable to the state-of-the-art real-time cache coherence protocol, and suffers a slowdown of 1.43x and 1.46x compared to the conventional MSI and MESI protocols.