Coconuts can be planted to create Palm Tree Saplings, but only on Barren (Beach) Turfs (The resulting terrain from digging up any other turf), and Sandy Turf, which can only be obtained in Deserts in the Reign of Giants DLC.
There is a 1% chance for Coconuts to fall when chopping a fully-grown Palm Tree on every strike, which equals about 14% chance for at least one Coconut to fall from every tree (when using a standard or luxury Axe), and about 1% chance to get more than one to fall while chopping it down. Each falling Coconut deals 20 damage to the player and it is left on the ground to be picked up afterwards, which can be used as additional source of food or to plant new trees. Falling Coconuts do not affect the regular drops from the tree, which will yield one Coconut and have 33% chance to yield another.
Two Halved Coconuts can be obtained by hacking a Coconut with a Machete. Halved Coconuts can be cooked over fire to obtain Roasted Coconuts. Both Halved and Roasted Coconuts can be eaten directly or used in a Crock Pot and provide a food value of 1 Fruit. Wildbores will accept and eat all variants of Coconuts, but they will not produce Manure for any.