This study examines how AI can rebuild governance trust and restore economic confidence in developing economies characterized by institutional fragility. Integrating New Institutional Economics, political trust theory, the confidence channel, and AI mediation theory, the analysis demonstrates that institutional fragility generates economic fear through policy unpredictability, corruption, and security failures, creating self reinforcing underdevelopment traps. Empirical evidence from Brazil, Rwanda, Kenya, Nigeria, and Venezuela shows that AI applications procurement monitoring, chatbots, revenue risk engines, and budget transparency tools can enhance governance performance, but their trust building effects are strictly conditional on institutional quality, data accessibility, digital literacy, political will, and civil society capacity. In enabling environments AI triggers virtuous cycles of trust and confidence; in fragile contexts it risks amplifying distrust. The study offers policy recommendations for governments and development partners to leverage AI responsibly.