I've been unable to find any part #'s or markings on the hardware. The thickness of the roller may be 5/16-3/8".
If you need more information about this part, I'll need to revisit the location the next time I'm in that neighborhood when I can catch the owners home.
Thanks for your attention. Your site is the best lead I've found on a part like this.
Paul from SWISCO responded:
June 2, 2016
Take a look at our 23-086. I believe this can work as a replacement for your older style closet door roller. Let me know what you think.
A quick learner from Springfield, MO says:
June 3, 2016
I believe we have a winner.
Will be ordering the product mentioned.
Thanks for your attention in helping helping me solve this problem.