I’d say there’s three specific requirements here;
- Allow users to choose notification times, timezone aware
- Hook into
transition_post_statusto listen up for new posts, and then take action - Find a decent SMS API
For 1), hook into show_user_profile to output your time picker field(s), and personal_options_update to save them.
You could detect the user’s timezone automatically, either via IP address or JavaScript, but I’d recommend just a <select /> that allows them to pick their locale manually (see wp-admin/options-general.php, lines 138 to 250 for how WordPress generates a timezone select).
As for 2), check out my other answer on new post notification. You’ll obviously want to modify this to notify all your users (as opposed to just the admin), but it should start you off nicely.
Finally 3), unless you can find an SMS API where you can specify the time the message gets sent, you’ll have to take advantage of WP Cron. Rather than setting an event for each user, I’d advise setting up an hourly one, that simply looks for any users who should now be notified & fires an SMS request.