No, nothing like this already exists.
You can always validate the date and force the user to enter a valid one before leaving the dialog.
Or use dropdowns for setting the day/month/year.
Or create a custom date picking popup dilaog.
What did you meant about "creating a custom date picking popup dialog" and how to acheive it?
You'll find a "pop-up" calendar here that you can copy and paste onto your PDF. Read the instructions carefully.
Thanks for your contribution, very useful. I had looked at your implementation but it is not so clear for me how to port that one on custom dialogs since there is no hidden property as it is for regular form fields in Acrobat. I guess it should be tricky to acheive it. so I hope I could port it later.