Best of luck searching for those hidden Easter eggs. 

They have been out of manufacture for awhile now. Older wheel. David at ClassicMinisJapan does come across them every now and then throughout the past years. Not sure where he gets them, he didn't/doesn't say. Not sue if they are new-old-stock that he's finding, refurbished ones, or being remanufactured in small quantities. Other than him, I've hardly ever seen them come up. They're more popular in Japan. So you could start hitting up sources over there. Here are some, if you don't already know. 

One other good source for Mini parts in Japan is this gentleman - Maruyama - San, owner of Mini Maruyama. This guy is a gem and knows a lot about Minis, racing, sells and collects rare parts, and so on. His English is fair to good. Good luck //minimaruyama.co.jp/index.html

Another Japan contact point is this place: //www.dinky.co.jp

Another in Japan is this place: https://turtle-trading.co.jp/british.html

Also in Japan, this one: //www.bonracing.jp

One other option, if you have the money, is to maybe approach a wheel manufacturer with that design and have them made. It would obviously be beneficial to make them in large enough quantities. But then every set you sell, is money back in your pocket. The Mini scene is picking up momentum, and the popularity of these wheels are making a come back as well. Could be a worth-while venture.

bikewiz, thank you for the tip, but they were one of the places that I contacted.  They said they did not have them available.   I'm curious as to whether these are wheels that are currently made or whether they are an older wheel now out of manufacture?  I can't seem to find much information about them.

Try David at Classic Minis Japan he has had Valtain wheels in the past and can possibly source them for you.
https://classicminisjapan.com/products/

Does anyone know where to buy Valtain (Vartan) 5J-10 or Type R 5J-10 wheels?  And, does anyone know where Valtain wheels are manufactured?