The java application would encrypt all information with the server's public (SSL) certificate (at least as far as you are concerned). For all practical purposes the only way to decrypt this afterwards is to know the server's private key which you apparently do not have and therefore there is no way that you can decrypt it.
To answer your comment about whether to use your computer's private key:
If this is a "normal" SSL connection, the client (java app) will contact the server and receive its public key, verify it's valid (signed by a trusted CA) and then use it to negotiate a symmetric key that is used for encryption.
Public/Private keys work in a way that everything encrypted by one key can only be decrypted by the other - i.e. everything the Java app encrypts using the server's public key, can only be decrypted using the private key - which never leaves the server.
SSL/TLS supports client certificates, in which the Java app can have its own key pair and use its private key to sign the contents in order to verify the authenticity of itself. However even if the Java app does that (doubtful) it does not help as the data will still be encrypted so that only the server can decrypt it.
Background reading: http://en.wikipedia.org/wiki/Transport_Layer_Security and http://en.wikipedia.org/wiki/Public-key_cryptography