Two nights is good - I even think three wouid be fine. We really enjoyed Copenhagen.
Ngaire, Denise and I (plus husbands) arranged to have a driver pick us up at the ship and take us on a tour of some of the castles outside of Copenhagen for the first day. The countryside was beautiful and probably merited more time.
Brad and I spent another full day there seeing the sights and took a final boat tour the next morning before our afternoon flight and we still had not yet seen some of the museums plus Tivoli.