Sylvie, I had no idea they wouldn't go through a pint in a day! I had read that normal sized chickens drank a tremendous amount--more than a person would think. If I put a bowl with rocks in it under the water, wouldn't the chicks perch on it and poop in it?
My standard hens drink about a cup and a half of water a day, each. They also free-range, so they're probably supplementing that with grass and bug liquid, so I figure a pint for a full-grown, egg-producing, standard-sized hen. Considering my hens weigh about six pounds each, that's proportionately pretty large.
I can keep ten standard chicks on a one-quart waterer from
TSC and only have to refill it once a day for the first week. That's a little less than half a cup of water per chick, including waste. Now, considering size, that is a
massive amount of water per chick, (the equivalent of my drinking seventeen gallons of water in twenty-four hours) but it's really not that much water.
And a bantam chick is about the size of the end of my thumb when it hatches. The chick might drink a little more than his weight in water, but that's still going to be less than a half-cup each by a long shot.
They will sometimes poop in the bowl, though less than you would think. I use large pieces of gravel so that they have difficulty reaching the water in the bowl, and I rinse it out at least once a day. There's probably other ways to do this, but this one works for me.
Hope your chick-raising is successful and that this was useful to you.
EDT: Okay, just re-checked your post. I thought you were talking about chicks, and just realised you were talking about full-grown bantams. (Sorry)
From personal experience, I'd guesstimate about half a cup each per day for my Old English Game bantams, but I wouldn't know about a large silkie bantam.
And quart-sized rabbit bottles are the only size my
TSC sells, so I doubt you'd have trouble finding a larger size. I suppose the selection might be different at
PetCo or similar.