Execute a Stored Procedure Daily
I'm assuming your DBA has not (and will not) give permissions for SQLServerAgent.
If so you will have to use another scheduler.

If you want to execute a stored procedure daily at a specific time, I'd suggest


Call the stored procedure from a page in your web application layer
Set up a scheduler to call the web page at a daily interval.


A free service like this could be set up to call your URL on a daily interval.
http://www.pingjs.com/