ZingChart does allow you to custom style the context menu using the contextMenu object. See the example here of it in action.

Example: https://demos.zingchart.com/view/OTMA5ZMJ

Within the gui  object you can configure the contextMenu  like so

gui:{
      contextMenu :{
        backgroundColor:'none',
        item : {
          backgroundColor : "#009688",
          fontColor : "#FFF",
          hoverState:{
            backgroundColor : "#00BFA5",
            fontColor : "#FFF"
          }
        }
      }
    }

Be careful though the gui  is outside the graphset of ZingChart as it applies to all the plots.

Note: On a mobile device context menus are not appropriate.  A hamburger menu is available in that situation which can be style as well.  See the context menu tutorial for information on that.

Documentation

Context Menu Tutorial
GUI Object JSON syntax
contextMenu JSON syntax

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