This waterproof vinyl label works well in ice and refrigerators. When applied to the bottle, there will be a small gap at the back where the two ends do not meet. The advantage of this is you don't have to worry about lining up the two edges. You may, however, need to remove the old label underneath.
The illustration below is not at actual size, but it shows you how this item compares in size to a credit card.
If you are not sure this size will fit your container, draw the shape on a piece of
paper using a ruler to measure, cut it out and lay it on your container.