In the October 10th Economist there’s a leader (“Wake up Europe!”, p. 13), on current events in the European Union, with some nice Euro- words in it:
[on the EU constitution] Some Eurosceptics want to fight on, hoping that a Tory victory in Britain could mean a new referendum.
[on the presidency of the EU] One could imagine, say, Angela Merkel sitting down as an equal with Presidents Obama and Hu; but she has another job. So the choice is the usual Europygmies or Tony Blair …
Neither word is brand-new. Euroscepticism and Eurosceptic have been around long enough for the first to get a Wikipedia page (where you can also find Europhilia). The Economist seems to be especially fond of Europygmy, but others have used it, since at least 2002.
(Spelling varies on these words. You can find Europygmies, Euro pygmies, and europygmies, and similarly for the others.)
Euro- words get their first element from the word Europe, and their second element is usually a free-standing word (as in Europygmy), though sometimes it’s a combining form (like -phile) or an element extracted from a larger word (like the vision of Eurovision, extracted from television). These words then often look like portmanteaus in their origin, but in any case act like compounds morphologically.
Michael Quinion’s Ologies and Isms has an entry for Euro-, with more details (including some items with the variant Eur-) . What it doesn’t say is that Euro-words have two accent patterns, differing in which of the two parts has the heavier accent: the first in Eurovision and Europhile, the second in Eurocommunism and Eurocentric. (Alternative accent patterns are well-known for many types of compounds.) I suspect that some people vary in their treatment of certain specific words, but I haven’t looked at the matter in any detail, nor have I examined the factors that are relevant to the choice of one pattern or the other.