Use two wall-mounted hooks and a rubber band to hold the roll of paper towels on a wall, refrigerator side or cabinet door.
The picture is quite self-explaining a few remarks will be helpful.
1. The rubber band should be a little shorter than or the same length as the width of the roll. If you can't find a band of a proper length tie two or more of them together.
2. The grey stuff you can see under the vacuum holder is UHU Patafix which allows to use vacuum holders on non-vacuum-holder-friendly surfaces like the side of my fridge. I already showed how it can be helpful in your car.