The data points of all scatter series have two double values which determine their position on the chart area. This limits the scatter series to be used only with numerical axes. 

DateTimeContinuous axes can be used with cartesian series. To achieve similar to scatter series look you can use LineSeries, hide the line of the series and leave only the data point points visible.
Here is an example code on how to set up such a chart:
DateTimeContinuousAxis dateTimeContinuousAxis = new DateTimeContinuousAxis();

LineSeries lineSeries = new LineSeries();
lineSeries.HorizontalAxis = dateTimeContinuousAxis;
lineSeries.BorderWidth = 0f;
lineSeries.PointSize = new SizeF(10, 10);