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Which app do you use? I'm using KeePassDroid, which seems to be the most popular, and as far as I can tell it only supports the clipboard method.

I'm not the person you replied to, but Keepass2Android [0] has the custom keyboard for password entry.

Sorry for the late reply, but I use this too (I wrote the original keepass post)

I use KeepShare, which has a custom keyboard for password entry, but also uses the accessibility APIs to auto-fill.