It would be a huge security hole to allow a non-admin to run an admin only app. Just think of what hackers could do with that kind of permission.
In order to run an admin-only app on a machine the user running it must be an admin. You can of course use UAC to have the user elevate or you can have the user right-click the app and select Run as Administrator and then an admin enter their credentials. Neither of these probably solve the problem you have though.
A hackish workaround that might work is to create a scheduled task that runs under an admin account and can be run manually. The user could then run the scheduled task which then runs under the admin account. Depends upon the app and your network setup as to whether this would work correctly or not though.
Of course if the user just needs local admin rights and you're fine with that then you can set up a GP to have an AD role added to the local administrators group. Then add the user to that AD role. That is how we give our devs admin privileges to their own machines.