For honeymoon I would recommend the following places to look at:
Catcha Falling Star
Tensing Pen
Rockhouse
Villa Sur Mer

They all have what you are looking for and are all fabulous properties.
If you want private I would pick Tensing Pen or Villas Sur Mer as they would be the most private of the choices as they do not have restaurant/bars open to the public like Catcha and Rockhouse do so there will be less traffic in and out of the resort.
Catcha is my all time favorite property (where we booked our wedding and where we now stay almost exclusively) and Sagi is my favorite room of all
We honeymooned at Tensing Pen in the Rock Cottage II and it was amazing
The Deluxe Villas at Rockhouse are awesome and are very similar to the Rock Cottage II at Tensing Pen