How do I provide fresh water for my two cockatiels when they keep peeing in both their water bowls?

You could get a water feeder for them. It is pretty much a water bottle turned upside down and with a straw in it, which should attach to th inside of your bird cage.

Put the water dishes higher than the perches and food dish and clean it daily. A big water dish is also great because they can use it as a bath. Again, just make sure you clean it daily.

You can get a water dish that hangs outside of the cage with an opening for their head to fit through but their body.

I use a regular hamster water bottle for my birds. They learned very quickly how to use it.