This is an old thread, but since it is still opened maybe you haven't found a solution yet. I faced the same problem myself and I think having the ability to manage contacts from the frontend is an essential feature for Joomla! to become more usable as a simple webapp creation tool.
Anyway, there are a couple of extensions that might help you out. However, both are commercial and don't support Joomla! 1.6. Here they are:
Front-edit address book: simple
interface. Note, however, that there
might be a security issue with
it. Google "front-edit address book exploits" and you shall find it (sorry, stackoverflow lets me post a max of 2 links per thread since I'm a new user). I emailed the developer and he assured me that the problem was already fixed, though.
Grumpy contacts: on the demo site (there's a link at the page I pointed you to), it looked a little messy to my taste. In the Joomla! Extensions Directory, however, it has good reviews.
I never used any of those since all my projects are already migrated to Joomla! 1.6.
If you found another alternative in the meantime or even developed something yourself, please let me know.