Following is photo of a recent find - from a 1912 J.S. Sullivan Saddle Tree Co. catalog. The foreword/intro of the catalog states that these are the more popular styles, and that these are kept 'in stock'. Any style they once had or that a customer would like could be made in a short time. So, we should safely assume that these styles (among the many in the catalog) were being made and sold as late as 1912.
Note, two 'Park' saddles are clearly Whitmans, but the Whitman name was owned as a brand by the Mehlbach (later Smith-Worthington) company. The 'Newark' style I've personally seen as late at 10 years ago being offered, as a 'Dragoon' style, as used by the NYPD. And the last candidate for discussion, the military style Jenifer - still available and sold as of 1912, as the 'Jenifer' style.
As time permits, I'll add a few other examples here that are somewhat surprising as well.
Longevity of style
The classic 'Spanish saddle', as found in 1912 - very nearly the same as the one pictured in 1850s, and described in 1830s contract letters - the primary characteristics being high cantle, tall slick-sided pommel with a medium sized horn, and a metal stirrup hanger attached very nearly at the base of the pommel. Earlier 19th representations have triangular stirrup hanger loops, this being the common rectangular style.