Is there an easy solution to the problems of Europe's south? Well, one of the eurozone's fundamental problems is that (a) workers in the GIPSI countries are uncompetitive and (b) the GIPSI countries are running persistent trade deficits. They need to import less while Europe's core (especially Germany) needs to export less.
So how do you make workers more competitive? One way is to simply cut their pay, but that's hard. Another way is to substantially reduce payroll taxes, which reduces labor costs without cutting take-home pay.
And how do you discourage imports? One way is to devalue your currency, but countries in the eurozone can't do that. Another way is to raise your VAT, which makes goods more expensive.
Put those together, mix in some more sensible monetary policy, and you get "fiscal devaluation" plus higher inflation. That's the recommendation of Georgetown's Jay Shambaugh, glossed here by Matt Yglesias:
Shambaugh also recommends increased ECB purchases of sovereign debt; capital injections into stressed banks; and bigger budget deficits in "non-stressed" countries. This all sounds surprisingly....reasonable. And even doable. It still wouldn't be easy, since there would very definitely be some losers from this kind of policy, but it's not flatly impossible. That's a start.