Aria here, I'm on the Social Care team at Shopify.
I found two apps that can help you with Print-on-Demand calendars. One of them isLulu xPress. They specialize in printing books of all kinds, including calendars. The other one I found isGooten. The benefit there is that they have a more diverse range of products, in case you want to dropship other Print-on-Demand products. You can find their product range ontheir website.
Do you just intend to sell calendars or will this be part of a range of products?