@adjmpw,
Irrespective of when you receive the data for charts, defining line chart as the second dataSeries and updating dataPoints of the respective dataSeries on receiving data from web-socket or AJAX should work fine in your case. Please take a look at this JSFiddle where dataPoints for 1st dataSeries, which is of type column, is updated after clicking the button.
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Priyanka M S
Team CanvasJS