var obj = {
  a: 1,
  b: {
    c: 2,
    notMe: "super secret"
  },
  d: 3
};

var str = JSON.stringify(obj, function replacer(key, value) {
  if (this && key === "notMe" && this.c === 2)
    return undefined;
  return value;
});

{ "a": 1, "b": { "c": 2 }, "d": 3 }