I have a wildcard certificate for *.example.com
(signed by GeoTrust) and am going to host lots of application instances on different servers, each on my subdomain.
I am not willing to copy my OpenSSL private key to every customer. How do I use my certificate to create sub-certificates for individual subdomains without sharing mine?
With some providers of SSL certificates (Digicert as one) you can generate new private keys and CSRs to request certificates on each server. This allows you to maintain separate private keys (and also generate these certificates for subdomains using Subject Alternative Names.). This does increase the administrative burden, but decreases the risk of sharing a single private key.
This is not possible. You either need self-signed certificates or you need individual certificates.