Currently in Beta, Kitely.com allows you to run your own private sim via Facebook. Initial hosting charges, once out of the trial period are very reasonable, and are built on a pay for use model. You can set access for your facebook friends but they are looking at other authorisation methods too. It's early days, but I am impressed with what I have seen so far.
Thanks for sharing this Lydia. This is SO cool although once created I kept crashing when I wanted to change a texture. This may be the kind of thing LL has been looking for to get intertwined with FB.