What is the avg minimum length of sun exposure to induce melanogenesis in a fair-skinned person assuming it is noon, no clouds, no sunscreen?

?: Highly variable - different for different people. Amount of sun absorption can't be quantified in a large study population. I'm sure there is no satisfying answer to your question. All we can say is that the more exposure you get, the higher your risk. The risk is much higher with each significant bout of sunburn.

Minutes : It would take only minutes. You should know this is a risky endeavor, however! Putting such a person in direct noon time sun will also result quickly in a sunburn, which will increase cancer risk! Unfortunately you can't get the melanogenesis without the risk! What are the goals of this project? To induce a tan? Hope this helps!