As a starting point, IMDB has a rather marvelous feature called "keywords" where users create tags for possible features of a film then tag films that contain such scenes or elements. It's a fun way to explore questions like this.
Sitting on a toilet (126 titles) is indeed such a tag. If we sort that list by date, the earliest "sitting on toilet" film is, apparently, a 1968 French comedy about cannibals who run a vegetarian restaurant (no, really!), called A Taste For Women.
If we take the list simply tagged "toilet" and sort it by date, IMDB believes the earliest film containing a toilet-related scene or plot was a German drama from 1924 called The Last Laugh, about a hotel doorman trying to deal with the indignity of being demoted to washroom attendant.
The earliest American "toilet" film does actually appear to be Psycho, 1960.
Here's a list of the dizzying, worrying variety of IMDB keywords that contain the word "toilet", which range from Head in a toilet (32 titles) to Toilet twerking (just one title...).
If you ever wanted to know the most popular film where toilet paper makes a notable appearance, according to IMDB, it's V For Vendetta. No, I don't remember the toilet paper scene, either, but some diligent IMDB user has tagged 148 films that include toilet paper. The internet is a wonderful and terrifying thing.
Researching this question has given me a very strange recent internet browsing history... Fun fact: I found out about this feature after a talk by director Edgar Wright, who described reading his own films' IMDB profiles and cracking up in baffled hysterics on discovering which elements the people of IMDB felt worth tagging. For example, Shaun Of The Dead has among its "plot keywords" "Cricket bat", "Arab grocer" and "Hip hop montage".