This has also happened to me several times, but the last time was yesterday after the latest upgrade. After opening Coast, I was met with a black screen and no sites! It appears that after a long period of stability, every setting was wiped as even my background photo was gone. I too, would like the procedure to restore my collected sites, if possible. My sites are indeed a collect that I have accumulated and categorized over some time. The ability to easily do this with Coast is a huge benefit. Coast is so superior to Safari that I find myself lost when I am forced to open it by the OS for a link.
I think there should be an easy way to restore sites and settings and to make them portable across devices. With the availability of Dropbox (et al) and iCloud, this should be fairly straightforward feature to code. I noticed I do have a backup of some Coast data in my iCloud backup and hopefully it can be of use to restore my sites. Any suggestions are appreciated.