You can use the UserAgent module to feed your existing cookies out to the correct websites (as far as I know). So if the cookie is persistent, just might try the CookieJar (i think) method to point to where the cookie resides.

If that doesn't work or the cookie expires after each session, then your Perl script needs to login. You just need to look at what their login form is sending in for authentication and mimic that. The UserAgent can handle both POST and GET requests.

In this case, I think the perldocs for the module are pretty good (even I understood them) and you should give them a real good eyeballing, since they will probably answer your questions.