You can do this with some automation tools (puppet for example), but to do it, you need to configure a working JIRA, work out which bits are "variable" (database connection, base url, Tomcat config to get it on the right url, proxy settings for web-server if you're using one, user directories, etc etc etc) and set up your preferred automation tool to be able to pre-prepare them.
As Nic mentioned, I agree that Puppet is a good way to do it. If I were you, a way to do it is:
Install JIRA in the standard way (by browser). Then, copy the main file configuration (server.xml, confluence.cfg.xml, database dump, etc) and create a script to automatize it on the next installation.
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