I have never seen a small bird with any type of a battery case, but that doesn't mean that you couldn't put one in, if you can find something that will fit the battery closely enough.
My 55, when restored about 10 years ago, had its top battery hold down frame modified to fit the more modern 6 volt batteries used today. And yes, I have had some minor acid issues, but only when charging the battery back up during storage periods. I've never thought to use anything other than the original bottom tray that the battery is fastened down to. I would imagine you could buy a close fitting boat battery case or similar, and cut it down somewhat to catch the offending acid runoff.