I'm Miles from the Social Care team at Shopify. I love the idea of creating a calendar for your customers. Although I don't know of a print on demand supplier that does custom events within the calendar, there is one called Gelato that does have a great wall calendar that you can include your own photos for every month.
Gelato is a great option as they have printers in 30 locations around the world in order to minimise the delay in customers receiving their orders. They also have a handy guide which walks you through how to design the calendar.
Some of the benefits of Gelato print on demand include:
You're also able to print and purchase at cost price yourself, so you can buy the calendars in bulk as well if you wanted to sell them in your bar. This would be super helpful for you to have stock on hand if customers don't want to pay for shipping or wait for their order.
All in all, I recommend checking them out. I've used them myself and can't speak more highly of them.
If you're still looking for a calendar, we'd love to help!
Contrado is a print on demand service and we have a range of calendars and catalogs that you can design.
Let me know if I can offer any more help!
Melissa from Contrado
Get the Contrado App for Shopify: https://apps.shopify.com/contrado-print-on-demand