Can mayonnaise be infused with coconut, without getting watery?
You can add some liquid to mayonnaise without breaking it.  I've added smallish amounts of soy sauce and hot sauce and such to mayonnaise with success.  The question would be, could you get enough coconut flavor into the mayonnaise before breaking the emulsion?

Hard to say without trying.

If it doesn't work, you can try using coconut cream instead of coconut milk.  Like the name suggests, coconut cream has a higher amount of fat and a lower amount of water than coconut milk. This should allow you to add more of it to the mayonnaise without making it too liquid.