On Day 6 of A Doo-Dad A Day challenge, I attempted to create these dispensers. In the crunch for time, I failed to correctly calculate the geometry of the dispenser and although the dispenser didn't work, the effort wasn't a complete a bust. The validity of the concept was proven, I just needed to do a little tweaking to get it right. Here is the result of another hour or two of design work and printing.
You can download the design file, thing741081 from Thingiverse.com. In the design, I included a single perimeter across the opening to act as support. This helps in 3 ways: it supports the overhanging dispenser lip to prevents it from sagging; it prevents warping of the upper curved surface during the print; and it prevents layer separation at the edges of the opening. This single perimeter support breaks away very easily and cleanly. I didn't have to do any finishing work like filing or sanding of the edges after removing the support. I could have allowed the Slic3r program to automatically generate the support, but I find that automatically generated support is too unpredictable and often difficult to clean up. It is worth the extra time to me to build support material into the design file.