Application Requires Admin Rights to Run

You'll need to debug with Filemon and Regmon, what the application is doing, that needs admin rights. It may be possible to identify, that it's right to a location on the disk or registry that requires Admin rights, which will allow you to make some changes, and grant access to registry and disk for those users.

Speak to the Vendor/Developer about the application, and see if they can work with you.

with scripting you could also try and install the application normally in any folder, and then use the subst command to fool the application is running in the root of a drive, but this doesn't help you with the Admin access.

that's write to a location on disk or registry (not right!).

There are no registry entries, just the files that are located in the program directory. Once I discover what files are needed for the app to run, is it simple enough giving the users admin access just to those files?

That is what process Monitor will tell you. Start recording as the user, open the application, when it fails, stop recording and review all of the errors. There will always be some that are totally unrelated, but it will advise which files, and registry entries, if any, the user was not allowed to access,and then you can add permissions for the user or a group  to which the user belongs.

It's possible it could be wrting to a temp directory? Check with Filemon and Regmon.

Filemon and regmon have been replaced by Process Monitor.

Thanks guys