It's TLS 1.0 that's broken, not SSL 1.0 ...
Well, SSL 1.0 was broken a long time ago, never use it.
With that in mind are there any browsers about that support TSL 1.1 and/or 1.2?
Yes Opera supports it very well. But this doesnt help you with IIS being the only common used web server with at least wacky and hidden support for it. So basically on the server side coverage tends to be zero.
Of course this may change now.