My cutter sits on a kitchen cart, and the back side of the cart has a towel bar. I realized I could make a shape to hang off the towel bar and hold a roll of vinyl. This took about $15 in 1/2" PVC parts from the hardware store, and screwed together even easier than I had hoped. I didn't even have to go back to the store to get something I overlooked, it was a miracle!
You could easily make a stand-up tabletop roll holder in a similar way, just make a frame that sits flat with "T" junctions to hold up a crossbar.