Painting the bird bath, advice please!!

I have a bird bath in my garden which is made of stone. The previous owner had painted the inside of the bath and the paint is now chipped. This makes the bath difficult to clean as the paint chips off and I worry about the birds who use it. I was planing to repaint it and I wanted to know if there is a paint that is recommended to use for this which is friendly to birds and might be less likely to chip? Or would it be a better plan just to take off all of the old paint and leave it as plain stone?

Thank you :)