I read on here recently about hard-to-get euro coins but cannot find the topic where I saw the link. Luckily I found the site again ...
http://www.fleur-de-coin.com/eurocoins/rare-euros
A summary - in year order per coin - from there (as their page is a bit all over the place) is:
- 1 Cent - France 2002, Portugal 2003, Cyprus 2013
- 2 Cent - France 2002, Portugal 2003, Cyprus 2013
- 5 Cent - Portugal 2003, Cyprus 2013
- 10 Cent - Belgium 2002, Netherlands 2008, Cyprus 2013
- 20 Cent - Netherlands 2008, Cyprus 2013
- 50 Cent - Netherlands 2008, Cyprus 2013
- 1 Euro - Netherlands 2008, Cyprus 2013
- 2 Euros - Greece 2007, Netherlands 2008, Cyprus 2013
Not sure how accurate the details of those 20 coins on there are, but hope it helps.