Video walkthrough of a W7 install: Installing SQL Server R2 2008 in windows 7 - YouTube
Known compatibility issues (not a big deal): Known issues installing SQL Server on Windows 7 or on Windows Server 2008 R2
And a total walkthrough and explanation of how to install SQL Server 2008r2 on Windows 7: Aaron Bertrand : Is SQL Server 2008 supported on Windows 7 / Windows Server 2008 R2?
I could imagine using some incredibly old scheduling or logging platform that you're trying to retrieve and use for archive finding purposes that was designed on, say W95 and for some reason isn't compatible at all with anything past XP... but downgrading to an obsolete OS (and not even up-to-date with SP2) for a modern and current, core Microsoft product just for compatibility with the install, is not smart in any way. That's like, Crysis 3 coming out and somehow only being compatible with DirectX 7 OR DirectX11, nothing in between and one of those versions leaves out almost every graphical feature the game uses.