Speaking from experience as an Irish historian who is occasionally forced to lecture in this period, I always recommend my students read beyond TP Coogan as, generally speaking, his works are indeed considered biased. In fact, his book on the Famine is generally viewed as something of a joke, which says a lot about some of his other work!

I would suggest Anne Dolan, Peter Hart (another contentious character, whose sourcing has been the subject of much debate) and Diarmad Ferriter for a more complete overview of the early IRA and Collins. I would then follow their footnotes and read the sources they cite, and you'll be able to build a comprehensive picture of 20th century Ireland.

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Hope this helps!