I think you ey need to do some sanding go remove shine so paint can adhere to table ,sand just a bit
use KILZ high bonding adhesion primer https://www.kilz.com/primer/kilz-adhesion or need to strip it off w/Citristrip gel stripper or remove by sanding
Wash down with TSP , then hand sand off the sheen using 220 grit sand paper . Prime with oil based primer. Lightly sand again if not smooth. Paint. For best results and most durable finish use oil based paint.
With chalk paint you can paint over practically anything.