Delay-coupled systems often require low-latency decisions from sparse telemetry, where dense fixed-step neural inference is wasteful and can degrade near stability margins. We introduce Network-Optimised Spiking (NOS), a trainable two-state event-driven dynamical unit for delayed, graph-coupled streams, whose states map to a fast load variable and a slower recovery resource. NOS uses bounded excitability for finite buffers, explicit leak terms for service and damping, and graph-local coupling with per-link gates and communication delays, with differentiable resets compatible with surrogate-gradient training and neuromorphic execution. We prove existence and uniqueness of subthreshold equilibria, derive Jacobian-based stability conditions, and obtain a scalar network stability threshold that separates topology from node dynamics via a Perron-mode spectral condition. A stochastic arrival model aligned with telemetry smoothing explains increased variability as systems approach stability boundaries. On delayed graph forecasting and early-warning tasks from queue telemetry, NOS improves detection F1 and detection latency over MLP, RNN/GRU, and temporal GNN baselines under a common residual-based protocol, while providing calibration rules for resource-constrained deployments. Code and Demos: https://mbilal84.github.io/nos-snn-networking/