It's a nice idea, but it was rather bulky and used more tiles to indicate the day than necessary. Most designs use 31 tiles, to represent the 31 days of the (longest) month. But, a distant memory of a Martin Gardner column, reminded me that only 12 are actually needed.
So I built this...
(ok - it's my first attempt, and I'm not that handy with card, but I hope this explains the method)
You will need:
Two blank dice
One piece of card
Some clear tape
Step 1: Create a template
You will also notice that many of the other sides need to have equivalent lines.