Nick here from Shopify.
I looked into this for you, and the print on demand apps within the Shopify App store didn't seem to have wine glasses, water bottles or tumblers as a common product. Because of that, you're best bet for this might be to look for vendors online. I did a search and found some possible suppliers which might work for you, hopefully, they do. Let's take a look at them:
Regarding custom wine glasses, it does seem like a print on demand model might be difficult to come by as wine glasses are normally sold in bulk to help save costs but also to assist with shipping. There are a few options I found for this which can be seen below:
Hopefully, something above can do what you need it to. It might also be worth your while to reach out to potential suppliers directly to discuss a possible on-demand model for selling.
All the best, Nick
Hi! I am in the process of setting up my Shopify site, but have my other website up and fully functioning. I have an online designer, which I am working on adding a similar one to my shopify site. I am not currently setup for drop shipping, though, I expect when you place an order I would just omit any mention of my company, and add yours. I would love to discuss this with you further if you are still interested.