Cups are certainly not a recent invention!
I’ve managed to track down references to menstrual cups and similar devices (back then they were called “Catamenial Sacks”), to as early as 1867.
1867 saw the invention of perhaps the first menstrual cup-like device. The Hocket Catamenial Sack consisting of an internally worn pouch like item that was connected to a belt. (why the cord and belt? I have no idea – so you didn’t lose it if it just fell out maybe? who knows). To empty it you would remove the pouch and reinsert it again afterwards. (Another reference to this design at MUM)
The designs of these early menstrual “cup” like devices are quite interesting and bizarre to us now.
catamenialpatents.wordpress.com/internal-products
While Leona Chalmers is often
credited as the inventor of the modern “Menstrual Cup”, I’d actually argue that others got there first. The first device that was not attached to any form of catchment bag, and was a single insertable device seems to be the 1903 Coke & Mallalieu device. While it doesn’t look like a menstrual cup as we know it, it is the first to perform the same function.
If we want to consider the first menstrual cup to be shaped similar to how we see them today, then the Norquist device would be the first. Having a somewhat art-nouveau appearance it starts to resemble a modern cup. 
Then in 1932 the Daintette and Foldene cups were patented, which are very similar to cups of today. The MUM has examples of these cups, so we know they were in production. Following those was the Chalmers cup in 1937. This cup (later called the Tassette) does have a very similar look to the modern Keeper and Mooncup brands of cup and appears to have been the most successful of the early cup designs.
Reusable Menstrual Products 