There are many security related reasons why this is generally a bad idea and there's nothing built into Windows to facilitate this in any way (short of creating a script and embedding credentials in the script which is just as bad of an idea).
If this is an absolute must to meet a business requirement, then you have a couple of options to my knowledge:
- Figure out why the app thinks it requires admin permissions and address those using a shim or targeted ACL change (or yell at the vendor of the software and have them do this as it's terrible form in general for a user application to require admin permissions).
- Buy a third-party product that does selective user elevation on a per-app basis.