Resolution
The given alias does not contain a private key.
Verify that the alias in the keystore is not a "trustedCertEntry" (public key). The alias should be of type "PrivateKeyEntry" which indicates that the certificate contains a private key and is suitable to identify a SSL participant.
You'll need to configure JBoss Web with a certificate with a private key (purchased from a certificate-signing authority or self-signed depending on your needs). See this knowledge solution for more assistance with creating a certificate suitable for identifying a SSL server or SSL client.
Root Cause
One common way this can happen is when importing the certificate returned from a Certificate Authority (CA), specifying a keystore that does not exist. Keytool will create a new keystore if you import a certificate into a non-existant keystore. You should import the certificate into the original keystore overwriting the original entry/alias with the private key.