Although Google Calendar doesn't allow you to create or modify arbitrary recurrence rules, the iCalendar specification which it uses and understands is quite robust in this regard.
Create an ICS file with a custom recurrence rule (RRULE). For example, for an all-day event on the first, third, and fifth Fridays of every month, starting 2 March 2012:
BEGIN:VCALENDAR
BEGIN:VEVENT
DTSTART;VALUE=DATE:20120302
DTEND;VALUE=DATE:20120302
RRULE:FREQ=MONTHLY;INTERVAL=1;BYDAY=1FR,3FR,5FR
DESCRIPTION:
LOCATION:
SEQUENCE:0
STATUS:CONFIRMED
SUMMARY:Event on the first, third, and fifth Fridays.
TRANSP:TRANSPARENT
END:VEVENT
END:VCALENDAR
To import the ICS file (updated June 2018): Click the gear icon and select "Settings", then choose "Import & export" from the menu. (Here's a direct link as of June 2018.) Under "Import", select your ICS file and upload it to the desired calendar.
For this example, Google Calendar parses the RRULE correctly and even describes the recurrence as "Monthly on Friday of weeks 1, 3, 5 of the month":
![Google Calendar event form showing recurrence rule reading "Monthly on Friday of weeks 1, 3, 5 of the month"](https://i.stack.imgur.com/VG0Jf.png)
Of course, you won't be able to tweak the custom recurrence rule from within Google Calendar, unless you want to replace the recurrence rule entirely with one of the standard options. Otherwise, you'll have to delete the event, tweak your ICS file, and reimport. You should still be able to make other changes to the event within Google Calendar, such as renaming, moving to another calendar, etc.
If this helps, you may wish to read more about the flexibility offered by custom recurrence rules in the iCalendar specification.
I was looking to do something similar for a 90-day workout routine. I ended up writing a simple bash script, using GoogleCL, that added an event for each of the next 90 days with the week and day number of the course in the title of the event.
Something similar could easily be done to count the age of your daughter. A search for GoogleCL should bring up needed info.
I guess the drawback is that the events are not "linked" like a recurring event is if you want to make a change later.
@digitxp Maybe this is an even nerdier solution?
Best Answer
I have done this many times, though only on Android. When you make a new event on Android, you go to Repetition and then type of repetition and then choose monthly, where you can specify a number day.
Edit: I just checked the desktop version for you, which works as well. When you make a new repeating event, first set it on the start day, then check the Repeat box, choose a Monthly event, and the option to make it a specific day is a radio button.