Cheap cup dispensers don’t last long, and quality ones can get a little pricey. Make a wall mounted cup dispenser for free with a tall beer can.
All you need to make one is a tall beer can (Instructables user Kamm65 uses a 24oz PBR), a can opener, clear silicone, a strip of hook and loop tape, sandpaper, a file, and a rag. Fill the can with water to support it while you sand off the paint and polish it. Use the can opener to remove the lid, and file the rim to smooth it out. Dab some glue on the inside of the rim to hold the cups in place, and mount it after it cures.
Mount it in a corner for the best support. This may not be the prettiest cup holder, but it gets the job done, and is easy to customise or replace later.
Beer Can Bathroom Cup Dispenser [Instructables]