We present an algorithm based on temporal-epistemic model checking combined with fault injection to analyse automatically the diagnosability of faults by agents in the system. We describe an implementation built on the multi-agent systems model checker MCMAS and a dedicated compiler for injecting faults into an MCMAS program. A diagnosability report is generated by the implementation which can be utilised at an early stage of fault tolerant multi-agent system design to ensure accurate fault diagnosis. We demonstrate the practical usefulness of the algorithm by performing automatic diagnosability analysis on a model of the IEEE 802.5 token ring LAN protocol which employs fault diagnosis mechanisms to achieve fault tolerance.