Can a Parked domain use a different SSL than the domain on which it is parked?
A Parked domain (Alias) cannot use a different certificate than the domain on which it is parked. This is because Parked domains share a virtual host with the domain on which they are parked. Only one SSL certificate can be specified per virtual host. Attempting to install a certificate for the Parked domain will replace the existing certificate for the domain on which it is parked.
However, a Parked domain may be converted to an Addon domain with public_html as the document root. Addon domains do not share virtual hosts. Converting a Parked domain to an Addon domain allows the domain to serve the same content and use a different SSL certificate from the domain on which it had been parked.