The execution of multi-agent plans often requires communication between agents in order to synchronize their tasks. In cases where communication is unreliable or undesirable, temporal decoupling algorithms allow agents to find a distributed execution strategy beforehand without requiring perfect communication on the fly. The state-of-the-art Multi-Agent Simple Temporal Network with Uncertainty (MaSTNU) framework extends the decoupling problem for Multi-Agent Simple Temporal Network (MaSTN) to allow the modeling of uncertain durations and allow agents to communicate when certain events occur and communication is available. However, the existing approach assumes centralized knowledge of the MaSTNU, whereas in the multi-agent context, privacy is an important concern. In this paper, we propose a distributed, privacy-preserving algorithm for finding distributed execution strategies for MaSTNU. Experiments also showed significant speed-up of the proposed algorithm when the multi-agent plan is loosely coupled and mostly private.