Contact tracing with mobile applications is an attractive approach for many governments and industry initiatives to address the Covid-19 pandemic. However, many approaches today have severe privacy and security issues, and many of them also fail to offer a sustainable contact tracing infrastructure due to the demanding energy consumption. This work makes several contributions towards overcoming these limitations. First, we propose a privacy-preserving architecture for contact tracing that leverages a fixed infrastructure of BLE beacon transmitters. Second, we evaluate the feasibility of adopting batteryless or energy-harvesting BLE beacons to make this architecture more sustainable and green. Finally, we identify practical research challenges and opportunities for academia and industry to advance and realize the proposed privacy-preserving and sustainable contact tracing architecture.