I love your outside entertaining area. It does need a color that would complement but give the area a focal point. I like the darker red,orange colors you may find in natural. You could dress up the table with accessories and place cushions in a complimentary color on the benches. Colored potting containers would also bring it all together. I like the uplighting here in the photo you could place along the back fence to add drama. Your area reminds me of Modern mediterranean landscaping.

I just found out that blue green colors really bring out the beauty of wood. I know its not the same but I have honey oak cabinets and just repainted my kitchen a blue green and it really made the cabinets look stunning. Maybe you could try something in that color family to enhance the wood. Just a thought.

I would go with a gold or yellow ... of course I happen to love teal/ turquoise and gold/ yellow together. Something in variations on the photos below... maybe some pink accents if you have a girl or lime green or blue accents if you have a boy.

I was about to say grey until I read the last line. What about a light brown carpet?