Finding decent coffee beans in FP can be a hit or miss. The following stores have been known to carry coffee beans
Maxi - Starbucks beans (Flavored - Vanilla, Hazelnut, etc). They do have large tins of ground Folgers coffee.
Careefour Papeete - stocks coffee beans
Champion - Papeete usually stocks coffee and some beans
Polynesian Trading Company (Kirkland Products) used to carry coffee beans (1-19)
Champion - Mo'orea (Viarae) often has coffee beans.
Super U Mo'orea Cooks Bay also stocks coffee beans but often sells out
But like anything if you see it buy it!
Let me know if you find other stores that carry coffee beans and I will add them here