Ask a fan of the show questions about the show. Do math to identify how many sets they use, how many guest actors and how many regulars. Ideally use fewer guest actors and fewer sets, so that your episode is cheaper to do. Notice the number of pages their script is and what pages the commercial breaks are. You might save TV Guides to look up what stories they've already done.
Some shows have complete episode guides on the web.
You might create a spiritual sequel. Not using their existing characters, which may cost them more money, but noticing a style of story they like and maybe out-doing that previous story. Especially characters that have been neglected. When one of those ideas gets funny or scary or otherwise makes you want to write it, write that down. You might show one of their regulars in a new light.