I don't know what could be going wrong. I have planted about 10 coconut trees in my town and I didn't water them or anything and they grow fine. They are on a green (well white since its winter) tile that is directly beside the beach.
To be honest they are not all that special. They pay 500 bells each but you can only get 2 instead of 3 from them. So all in all better to just plant some more uncommon fruits. I still keep mine around for collectors sake. Now if I could just get my hands on some cherrys.
Well you need to plant them on the shoreline. Thats the place where land meets the sand. Thats the perfect spot because the coconut is getting the best of both worlds. You get a good percentage of it growing, when in right spot.
The best bet to grow trees is by cutting down trees and then replacing it with the new one, it always works trust me (I replaced many trees yesterday and they all made it)
Also, I have 16 coconut palms, and I just planted them randomly... but of course I planted them near the shore and yet not so close like planting in the sand