hi Jinty
I am afraid I cant help you with recommendations for private apartments in the centre of Protaras,
There are plenty private ones just further along in the Kapparis/Pernera area . I understand about the 2 ring thing its a nightmare if you take a family, we went with our grandchildren a few years back when ours was being built and we decided to go private to get a feel for it so to speak am I glad we did the youngest was poorly and vomited from the minute we got of the plane until 2 days before we went home, Was i glad we had the washer , and full size cooker to use , we could.nt even go out for a meal as she was that poorly.
I cant think of any with more than 2 rings though, we did S/c at the Brillant years ago and found that was adequate , but i cannot remember what the cooking facilities were like, but in all that heat i dont think you eat as much anyway but the bottom apartments that faced away from the pool had lovely big balconies. and the pool area was all level with no stairs we liked it in the Brillant handy for the strip and beach but set back a bit away from the noise.