You are correct that that is not an advertisement for birth control. It is not even from the nineteenth century! It is a humorous postcard of the early twentieth century - it's post-1907, when postcards began to be designed with extra space on the back for writing your message, instead of a white strip at the bottom of the front or a kind of fade to white at a lower corner, and is probably from about 1910 or within the first half of the following decade. Postcards absolutely boomed between 1907 (due to the aforementioned development of actual writing space) and the outbreak of World War I (due to the fact that postcards had been often imported from Germany), and every kind of theme or style was available during that period - jokes, religious images and quotations, pretty flowers, landscapes, and saucy photographs.