Usually japanese readings are used for the first 10 days like ついたち、ふつか、etc.
Japanese wiki here shows readings like ごにち, ろくにち.. (You can just change the number in the url before the 日 to navigate). So are those used anyhow?
いちにち is always used instead of ついたち to refer to a duration "one day".
仕事を一日【いちにち】で終える to finish the task for one day
ににち~じゅうにち are much rarer, but can appear as part of phrases like [二、三日]{にさんにち} or [五、六日]{ごろくにち}. I don't think 二日 by itself is ever read as ににち.
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