Have you tried to run 'at'? Do a man at to see what it does. It is basically a one time cronjob... ie. $ at 5:30 ./run_me_at_530.pl

Perhaps each time your script runs it can re-at itself... run the same at command so that it will execute the next day. Not a very maintainable solution, but if it's one script, and they have the program available, it might be useful.