Use a screwdriver to gently remove the screws holding the coat rack in place. Remove the coat rack from the wall.
Insert a bigger screw into the coat rack if possible. This will ensure a tighter fit when you screw it back into the drywall, meaning less chance of it becoming dislodged and wobbling.
Buy a wall anchor if a bigger screw is not feasible. The wall anchor should be the size of the hole in the drywall. Insert it in place by simply tapping it with a hammer until it is flush with the surface of the drywall.
Re-insert the original screws into the coat rack if you inserted wall anchors. Screw the coat rack back in place, firmly inserting the screws into the new wall anchor, which should hold it much more securely in place.