Since CF 9.0.1 IIS7/7.5 is supported, so you will face compatibility issues
Yeah, can you really expect a program designed to run on Windows NT 4.0/IIS 2/3/4 to run on an operating system released more than 8 years later? IIS 7 (the version in Windows 2008) was completely rewritten, so it will not support older web application servers.
If they can't afford to upgrade to CF10/11 (and I suspect it would not be an "upgrade" license, it would be a full purchase as CF4.5 is not in the supported license upgrade path), have you considered Railo as an alternative? I wouldn't expect it to have any more problems than CF10/11 running "legacy" code from CF4.5.
I was able to set CF 4.5 on Win2008 a while ago. It worked. But I didn't test it deeply. But cfm pages were being processed. Installation of 4.5. setup will fail with the handler installation. You'll have to enter the handlers manually in the handler-module and assing the dll to the cfm pages there. I think isapi-extension have to be added in the IIS-Feature.