After installation of a wildcard SSL certificate into the certificate store, the certificate does not appear in the IIS certificate list for use with site bindings.
had the same problem.
You need to ensure you are installing on the same server as the one you created the "CSR" file from. Otherwise, it won't have the private keys.
If you got your cert, just ask to re-key, it will ask for a new CSR file. I.e. Go Daddy allows you to re-key, just find the cert, and hit "manage"
I am not expert at this stuff, but this managed to work.