Have you checked gems on display. They have a nice inexpensive pen box. But they also have Jewry boxes of all sizes. I am not sure but they may have one that would fit a stopper. Of course you might have to order bulk.
I prefer to use velvet pouches for bottle stoppers. And the cheapest I have found are at a site call Aliexpress.com, which is an online retail service based in China that is owned by the Alibaba Group. Launched in 2010, it is made up of small businesses in China and other locations, such as Singapore, that offer products to international online buyers. For large bulk orders, the parent company runs a site call Alibaba.com.