Tranquility Bay is phenomenal!!!! No rocks for sure, great beach. you can snorkel to the reef, and it is so far North (12 miles apx)c/o depends on who is staying there that week. There are some very isolated spots way up there!! Great place, great people!!!
What about Hotel del Rio? Isn't it still up and running? It has one or two individual cabins, IIRC. For the original poster, this would be more budget style accommodation than Victoria House, Ramon's, Mata Chica, Portofino or Capricorn.
A fish and a bird can fall in love, but where will they build their nest?