Expanding on the dispenser line, this fits 9 ounce Solo cups such as these.
https://www.amazon.com/Solo-Party-Cups-Blue-50/dp/B00CESQA7I Please make sure this is what you are looking for and not the bigger party cups that are 18 ounces from my other listing. I have not tested this with any other 9oz cups at this time. This is mounted to the wall with two screws and can be use with wallboard anchors or screwed into wood.
I can make these with hidden or exposed screw holes. I find that the hidden version works fine, but may need a bit of a longer screwdriver to install. If you are concerned with accessing the screw holes, choose the exposed option. I've shown photos of both.