I took a quick look on the Google N-gram Viewer, which I’ve found to be a useful (although occasionally misleading and frustrating) reference tool. typically, it doesn’t give dates in the 1920s, as others have unearthed.
But, to my surprise, there are examples of “Porcelain Throne” dating back as far as 1848! Only these refer to an actual, royal king’s seat made out of porcelain. The references place these royal sieges in India and China. I wonder if people began referring to a “porcelain throne” not from their own coining of an ironical term by combining the porcelain of an existing toilet with the idea of “throne”, but by using recollections or occasional references to such actual Porcelain Thrones, seeing the ironic possibilities therein, and using the term directly for “toilet”. It would be much the same was the term “Sultan of Swat” , which was an actual* title of an Asian ruler, was applied to Babe Ruth – they took an actual title and applied to to Ruth – they didsn’t create the alliterative title “from scratch”.
*actually, the original references were to the “Akhwand to Swat”. I suspect it got changed to “Sultan of Swat” because most Americans don’t know what an “akhwand” is (I don’t), and for its alliterative value. And Babe Ruth probably would want to be called an “Akhwand”, anyway.