I just happened to have started my home business application in windows forms for the convenience. I'm currently using Visual C# Express 2010 / SQL Server 2008 R2 Express to develop it. I got the same problem as OP where I need to connect to an instance of SQL server. I'm skipping details here but that database will be a merged database synched between 2-3 computers that will also use the application I'm developing right now.
I found a quick workaround, at least, I think I did because I'm now able to use my stored procedures in tableadapters without any issues so far.
I copy pasted an SQL connection that I used in a different project at work (VS2010 Premium) in the app.config and changed everything I needed there. When I went back to my Settings.settings, I just had to confirm that I wanted what was inside the app.config file. The only downsides I can see is that you can't "test" the connection since when you go inside the configuration of the connection string you can't go anywhere since "SQL Server" is not an option. The other downside is that you need to input everything manually since you can't use any wizards to make it work.
I don't know if I should have done it that way but at least I can connect to my SQL server now :).
EDIT :
It only works with SQL Server 2008 R2 Express instances. If you try with SQL Server 2008 R2 Workgroup and up, you'll get a nasty warning from Visual C# 2010 Express telling you that "you can't use that connection with the current version of Visual Studio". I got that when I was trying to modify some of my tableadapters. I switched back to an SQL Express instance to develop and it's working fine again.