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My Samsung has Українська available as a full settings language. I would expect most major brands would have the same.
Third party keyboards like SwiftKey, if like me he doesn't like the stock keyboard, will have Українська available to download.
These are very clever people. Mind you, I live in UK with a European Samsung Galaxy Note 3, but I would assume US and other versions would have this built in also.
So you should be good with a Samsung Tab, Tab S, Tab Pro, Note and Note Pro series.
Pop in to a store and check the Language and Input screen.
On Edit: I add another screenshot. I don't fully understand how Cyrillic script works, so if this solution above does not solve the issue, I would be grateful to know.