You have a couple of choices. Number one is to sand down the shiny surface of your table. Another is to use a primer then a paint on your table. The third choice is to use a chalky paint of some kind that adheres to the shiny surface with little or no prep. I always sand lightly anyway. Here is just one tutorial you can find on pinterest for using chalky paint. https://www.pinterest.com/pin/15340454968106109/
Juli: using a chalk paint, with distressing will give you and aged, loved look that will only get better with time. It has a non-sting finish -- and you seal with wax coat.