Coming from a professor in a different department...there's so much flexibility with directed studies. They range from 1-4 credit hours and you're, of course, expected to do more work the more hours you sign up for. My best recommendation would be to talk to the professor(s) with whom you think you'd like to do the directed study. You can talk about what you're interested in, his/her ideas for the semester, and so on.

That you're this close to graduating means you've likely developed relationships with professors in the political science department over the years so I'd drop by their office hours or shoot them an e-mail. Some professors may not be amenable to doing a directed study (as it requires work on their part), but there's no harm in putting out feelers.

With regard to the syllabi question, I've never used a syllabi for a directed study. Rather, students and I have worked on research projects together over the course of the semester, as their schedules allowed. I'm a huge fan of directed studies -- I love that I can tailor projects to students' interests and/or skill-building goals.