Can I use the same SSL certificate for a Tomcat service on port 443, and for a separate IIS service on some other port? Both services live on the same machine, on the same IP address and have the same DNS entry.
If so, how would I convert the certificate (issued for Tomcat/java) to a form that IIS7 can handle?
Yes, absolutely - those services can both use the same certificate.
Can you clarify what format the certificate is in now (in a java keystore, or x509, or maybe pkcs12)? We can definitely provide some assistance in getting it converted with further details.