Hi,
Yes it is possible, by default subdomains have a private_html directory (the subdirectory for the subdomain is created in both public_html and private_html). However having said that it will then use the shared SSL Certificate of the domain or the server.
To set it up with it's own SSL Certificate you need an IP Address dedicated for this subdomain. Create a new DA Account listing the subdomain as the domain for this account. and assigning a dedicated IP to this account.
Regards,
Onno Vrijburg