Give an example of a law that would be constitutional per se, but unconstitutional in its application in specific instances.

One example of such a law could be a death penalty law. 
In fact, in Furman v. Georgiain 1972, the Supreme Court ruled that
death penalty laws could be constitutional per se but could be unconstitutional as
applied to individual cases.

In that case, Justice Stewart
held that the death penalty itself was constitutional, but that it was being applied
unconstitutionally.  This was, he said, because the law was not being applied in any
sort of a consistent way.  Instead, he said the laws were applied in ways that made them
seem capricious and arbitrary.

So, a law giving the death
penalty for specific conduct might be constitutional per se, but be unconstitutional as
applied if it is not applied consistently to all defendants.