Answer: Unfortunately, there is no "category" of thornless or near thornless roses. Instead, they are spread throughout the different classes. To make things more complicated, the so called thornless roses may simply be less thorny than most, or the lack of thorns may be a bit variable. So while the "thornless" roses do exist, they will not usually be listed separately. Here are some to consider or ask about when contacting rose suppliers.
Golden Century, Sweet
Sunshine, Pinkie, China Doll,
Gruss an Aachen, International
Herald Tribune, Katharina
Zeimet, Verdun, Pink Rosette,
Basye's Blueberry, Marie Pavie,
Smooth Angel, Mrs. Dudley Cross, G.
Nabonnand, Nur Mahal,
Heritage, Paul Neyron, Reine des Violettes, Smooth Prince,
Smooth Lady, Smooth Velvet, Smooth Melody, Smooth
Aimee Vibert, Weeping China Doll, Climbing
Pinkie, Zephirine Drouhin, Kathleen Harrop, Crepuscule
Rose stocks will vary from year to year and also occasionally sell out early, so it worth asking a nursery if they have any thornless or near thornless varieties available. In the meantime, you may be able to locate some of the above using the rose finder at http://www.HelpMeFind.com/sites/rrr/rosetest.html or by using a rose name in quotation marks as a search term in a search engine such as dogpile.
Good luck with your hunt!
Q&A Library Searching Tips