Have you tried looking at the works of artists/photographers/engravers known to be active during the periods you are wanting to build a diorama for? After a quick general google image search of 19th century equine art you might try looking at works by George Stubbs, Edward Muybridge, Otto Eerelman,
Rosa Bonheur, and Edward Lamson Henry. That would probably be a good visual reference so that you have a basis for judging which sites are more accurate.

And because I was intrigued by how you might narrow things down and find some more trustworthy hard-copy research here's the Carriage Museum of America's website which seems to have a research library semi-available to the public that is willing to field questions; http://carriagemuseumlibrary.org/

The carriage collection of Long Island's online catalog for some visuals; http://www.aaqeastend.com/contents/portfolio/long-island-museum-carriage-collection-finest-collection-of-horse-drawn-vehicles/

My suggestion is to find a reputable and dated collection of vehicles like these two sites, or visit a collection/museum if there's one nearby, and pick a cart/carriage that has a named style and/or known manufacturer and narrow your research perimeters down to just that one rig to see if you can find documentation or even recreations of it in use.