Diamonds are rare and can be found in various ways.

Digging

You've got a slight chance of finding diamonds by digging.
There's a better chance of finding diamonds in the Mine.
The chance increases even further if you're VIP

Tag

Diamonds might pop on the floor while playing tag.
Read more about palying tag here: Tag Tutorial

Chests

You can also find diamonds in chests.
Chests can be found by digging or as an award for winning in Meow Games.

Daily Awards

Once a week, your daily award is a diamond.