How can I automate copying DB2 table data between remote Servers?
I think you may have answered your own question. I would use command line shell scripts. Seeing as you are on Linux, you have several to choose from (sh, ksh, and perl to name a few).

Another thing that could make things easier is if you catalog the remote server and database locally. Then you can connect to it and work with it without your script having to worry about ssh'ing over to another box.