Drawing on the experiences and lessons learned from researchers based in low- and middle-income countries (LMICs) that leverage generative artificial intelligence (GenAI) technologies to address socio-economic challenges, we showcase the considerable potential to use GenAI to accelerate the progress towards achieving some of the Sustainable Development Goals, as well as considerable obstacles for creating locally adapted AI tools for fair development in LMICs. An expanded evidence base on GenAI in resource-limited settings is crucial for policymakers to understand opportunities and risks, while rights-based safeguards against AI harms can be strengthened by the lived experiences of local projects.