There are usually mugs provided in the tavern, but if you want your own like attached to your belt, then you'd be surprised at what is acceptable. I have heard of some people with camel backs hidden under their clothes along with the hose hidden, and taking a drink briefly and hiding it again. If you can find metal water canteens or a plastic one and cover it with leather then that would probably be fine too.
Ok. Cool. I an a large man and sweat like a champ and wouldn't feel right about going out on the field without water. I got a couple ideas to try. Thanks all.
Do your best. But, if everything goes wrong and you can't find something appropriate, safety takes priority. You can drink straight from a Aquafina bottle if you need hydration and nobody will say a word. The game appreciates any effort you take to be in-period, but will never risk your safety over that.
What Mike said. If it's beastly hot, especially in oh, I don't know... all black leather armor? We will pretend we don't see the giant OOG water bottle. Hydrate. Please.
Note on canteens, I love mine but keep in mind that a corked canteen doesn't double well as a sports drink container. At least once an event I end up wearing the contents because I hit it reaching for a pouch or rolled across the field.
A screw top flask does not have this downside. I had to go on eBay to get a 16oz completely plain flask, but it wasn't expensive. If you're into crafts you could make a holster for it.