Update: this one works fine on the RX1 and is very secure, but it is difficult to operate with the lens hood. For compatibilty with the lens hood, get a center-pinch lens cap.
Update - Only the 49mm lens caps that are secured against the inner diameter of the lens, such as the snap-on lens caps, will work on the RX1 The 49mm lens caps that are secured against the outer diameter of the lens, such as the push-on lens caps, DO NOT WORK ON THE RX1.