Recently I have started using a little trick to keep moisture from forming on a dough ball stored within its container (covered) in the refrigerator, even though the dough has been coated lightly with oil. It is possible to allow the dough to dry out a bit before covering it in the refrigerator, as is done by pizza operators when they cross stack their dough trays for about an hour or two in the cooler, but there are times, as with a Lehmann NY style dough, where I want to get the dough into the refrigerator and covered as soon as possible so as to retard the fermentation process.
The trick entails placing a sheet of absorbant paper towel, folded in half, between the container and its cover, and pressing the cover down on the container so that the paper towel is tightly lodged between the cover and container. This is shown in the photo below. In using this technique, I have observed that the paper towel will be moist after a day or so in the refrigerator. Also, some moisture will form on the cover itself, between the cover and the sheet of paper towel. And the dough remains dry.