They make kits to paint over ceramic tile. Sold at Home Depot
Hi Phyllis. I gave my own kitchen backsplash a makeover which included painting the tile. I hope it will be helpful to you.
I painted my kitchen backsplash in just a few hours. It was one year ago and it still looks as good as the first day. Here are the instructions. https://thewoodspa.com/2017/08/18/painting-my-kitchen-backsplash/