When painting an old coffee table. Do I need to strip the old varnish?

If you use chalk paint you don't need to strip the finish. I use this recipe for homemade chalk paint... Mix 5 tablespoons of Plaster of Paris and 2 tablespoons of water. Mix well. Add to 2 cups of paint. Paint light coats, sanding after each application. Top with a wax or polyacrylic. Also...I buy the sample paints from Menards because they are under $3. Divide the plaster and water in half and it's just right for one of the samples.

you should but i believe if you use a primed you don't read the can it will tell you

No. Just lightly sand to remove any gloss. Prime with a good stain blocking primer like Zinsser 123 or BIN. Then paint with your color. Use a small foam roller and foam brush to get a smooth finish. No brush marks.