Hello Anatole,
I believe from your description that this item with a stand was not unlike that included in Remco's SNEAKY PETE MAGIC SETS. Yes, the card trick--very good for what it is--was available from the assorted D. Robbins-like sources of the time without a stand.
The stand is best described as being a diminutive reminiscence of the full size tiered racks used to hold real swords horizontally for the daredevils who used to walk on same barefooted.
I can't imagine any stock item from a non-magic source today being appropriate for this application. If I wanted to have a stand today, I would have a small block of wood (or Lucite) with 3 slits cut into it to hold the cards upright.
Perhaps there is a stock business card display available now that might serve the purpose?
Not much help, I know, but just responding for the clarification of anyone else besides you & I reading this at some point in time.