This proposal is vague and we would need to work with you to narrow things down a bit.
Yes, that would be cool :-) Since I'm not familiar with Persistence at all (unfortunately :-( ), do you have some suggestions for me to start with?
I've found this http://www.yesodweb.com/book/persistent and I'm going to get familiar with it in the first place. I hope it won't take me much longer than a couple days.
That is definitely the best place to start. If you want to look at more example usage code you can look at the test suite in the persistent-test folder of the repository. Perhaps you have a Haskell program that could benefit from persisting data (and maybe already does in a flat file) and you could try integrating Persistent with it.
I am rather far away from Web programming, so, unfortunately, I am not sure whether it would be relevant if I volunteered to contribute to Yesod directly. In my perspective, there are possibilities for a non-Web programmer to contribute to Yesod, though, so, if I am not too much off with my perspectives, I'll be glad to work on Yesod as well.
I also opened up a GSoC ticket for making Haskell ready for the "real-time" web. This is also another somewhat self-contained project that does not really require web development experience. More and more programs would like to have a web interface or at least speak some HTTP at some point. Most web programmers don't have a great understanding of the internals of web development that they are abstracted from. I wouldn't shy away from something web related because you are afraid you won't be able to hack it. The only problem would be that you might not be able to judge the project well before starting the project.