IMO...
No fake grass. Yuck. No rocks. Yuckier! Establish your goals first: do you want something amazing looking? Or do you need more deck space? What is the budget?
Looks like you already have quite a mashup of concrete: old, stamped and coping. Unless you can find a concrete guy that can match one of those, it's going to look like what it is: a quilt of concrete done at different times. So the solution, aesthetically, is to use contrasting material. Pavers would qualify, but yes, even that will likely look a bit weird with all the other concrete textures you have.
This is how I'd do it: remove grass and existing "decorative border" and extend the existing landscaping out to the existing concrete. Look in mag's for beautiful landscaping ideas, use contrasting heights and textures: shrubs, ground cover(s), perennials, etc. Then add some landscaping lighting, both up- and down-lighting, and you'll have a stunning backdrop to your pool, both day and night.
If you need or want to keep a sitting area, I'd build a Trex deck, raised 6" or so, back in the corner (with the new landscaping surrounding it). If there's not enough room for the chaises, switch to upright rockers or bistro table and chairs. If there's just barely enough room for chaises, and you're determined to keep those back there, you can extend the deck over the existing concrete a bit to accommodate them (how much depends on how much concrete decking you want to leave). Conceivably, you could build that deck all the way out to the coping, and really create a new look. That might interfere too much with the traffic to the slide, but the point is the Trex deck does not have to conform to the existing line of the concrete.
The landscaping (with or without the Trex) will be a natural extension of your existing flora back there, and won't clash with any of the existing concrete, and will be a lot prettier to look at than rock or pavers or concrete...
