Assuming you have your site hosted/built somewhere where you can schedule CRON jobs I would do the following.
Choose an interval you feel is "regular" enough (once every 15min/once every hour/ once every minute)
Create a php file that, if fired from the command line (>php some_email_function.php) would do everything you want it to.
Create an executable shell file:
#!/bin/bash
php some_email_function.php
..and schedule it in CRON to fire when you want it to.