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Banamine is safe for bunnies but they can be extremely sensitive to it and it can cause severe GI problems so I would not recommend it. The best thing to do is to just clean the broken nail area with peroxide a few times a day. I would not put anything topical on it because that may make the bunny lick excessively. If over the next 48 hours it looks like it is not healing he can have Trimethoprim Sulfa antibiotic if you have any. However, usually a broken nail does not come to this and just by keeping it clean and changing his bedding frequently, he should be fine.