iCal No Longer Runs Scripts?
I wrote an answer to a question about scheduling jobs that could solve a few of the issues for you. That was mostly for a one off time though versus ongoing.

If you have an ongoing job, like one that you would have scheduled through iCal, launchd will work nicely as well. 

But if you want an outright replacement to something similar to what you did with iCal/Calendar, it sounds like this great writeup on the Apple Discussions board explains using Automator's 'Calendar Alarm'. One user even said that this new way is even easier to use. I personally think with the extra power of Automator, it also adds new power.

From that site:


  Here's a solution that works for me:
  
  
  In Automator, create a Calendar Alarm
  Select Utilities from the library pane
  Select &amp; drag Run AppleScript into the workflow area
  Copy/paste the AppleScript into the Run AppleScript box
  Save the newly created Calendar Alarm
  Open Calendar.app, create a new event
  Select the Automator calendar as your reference calendar
  Select Open File for the alert, and select the file you created in Automator. By default, iCal is the file that comes up when you select
  Open File. 
  Change that to the name of the Automator app you created. 
  Select Other if the file name isn't shown.
  




The user attached some screenshots to their post, as well, but I have included a screenshot of what needs to be selected in Automator.