Yes, health insurance cooperatives are a good alternative to public insurance, because they more or less operate the same way. Those participating in the cooperative have slightly more say in what items are covered, and they can choose to exclude items covered by a poor lifestyle, such as drug treatment. However, cooperatives more or less function as appropriate medical insurance.
Co-ops are not a good alternative to public insurance. Co-ops would still be run by private organizations, so they would still suffer the same issues that the current private insurance companies give us. Public insurance should be the way to go in the future, and not trying to develop other ways for the consumer to get screwed.