On-demand delivery is a fast developing business where gig couriers deliver online orders within a short time from merchants to customers. Couriers' accurate indoor locations play an essential role in the business. Most of the existing indoor localization methods cannot be applied in practice due to the high cost or data unavailable on off-the-shelf smartphones. This paper explores a new angle to solve the problem in a relative and infrastructure-free fashion. We design a person-to-person localization system that can (1) detect encounter events via Bluetooth on couriers' smartphones, and (2) infer couriers' relative locations to all the indoor merchants via deep learning on a graph neural network. The system is infrastructure-free, map-free, and compatible for off-the-shelf devices. We deploy the system on a real-world industry platform. The system runs on the smartphones of 4,075 couriers around 79 merchants for a month. The evaluation in a mall area shows that P2-Loc improves the mean average error compared with state-of-art infrastructure-based, report-based, and encounter-based methods. We also use an application analysis based on real-world orders and trajectory data to show that the P2-Loc can save around $40,000 for the platform every day with improved indoor localization results.