Cyprus' banks should be saved by depositors, because the people who have a vested interest in the private businesses should do the rescuing. Also, the banks are more likely to make lasting changes and get their acts together if they have to answer to the people supporting them directly, rather than to a nameless and faceless government. Private is best.
In an ideal world the government can keep its hands relatively clean of the affairs of corporate interest. The Cyrups banks would be better off being saved by the depositors that would use the services of the banks, rather than relying on the bureaucracy of government intervention in their affairs.
It is the duty of the government to bail out a nation's banks. In the case of Cyprus, the government should use its financial power in order to help the economy recover. The nation is too risky for private investors to provide a bailout. Rather, the government should take responsibility.
I believe it is neither Cyprus's depositors nor their government that should save their banks. I believe if a bank does not function properly then it should be allowed to fail. I do not believe the United States truly benefited from saving their banks and don't think other countries will benefit from following in our footsteps.
The government bailing out Cyprus has benefits since much of Cyprus's business are international. I think that even though the government may bail out Cyprus, also private business owners may work with the government, and depositors that have large amounts of money may have a say. But the government should lead it.