When you install DotNet 2.0 on Windows Server 2008 R2 you will get an error saying:
You must use the Role Management Tool to install or configure Microsoft .NET Framework 2.0
Unfortunately the Role Management Tool doesn’t list DotNet FrameWork 2.0, so to install DotNET 2 on Server 2008 R2 you have to install DotNET 3.5 (which is backwards compatible with DotNET 2.0 applications). To install DotNet 3.5, go to Server Manager and add DotNet 3.5 Feature (this is actually the Role Management Tool that the error talks about).
If you are using a web application with IIS, there may be additional steps to take such as registering DotNET 2.0 with IIS or ASP, etc…
This obviously isn’t perfect, because not all DotNET 2.0 applications work nicely with DotNET 3.5 or above, but it’s the only way to “install” DotNET 2.0 on Windows Server 2008 R2.
If your application doesn’t work with the newer version of DotNet, your only options are to get a newer application or an older operating system (that will eventually become unsupported by Microsoft and get smothered in lovely viruses). In essence, in this scenario I recommend updating your DotNET 2 application.