In your case (only single point per X-axis value) you should be able to get JMP to record a script to you and use that

More robust option would be to add second plot to your graph (float bar chart with 0 line width) and label that

Script you can run to test out how it is done and how it looks like in JMP
Names Default To Here(1);
dt = Open("$SAMPLE_DATA/Big Class.jmp");
gb = dt << Graph Builder(
	Size(769, 776),
	Variables(X(:name), Y(:weight)),
	Elements(
		Points(X, Y, Legend(3), Summary Statistic("Mean")),
		Line(X, Y, Legend(4)),
		Bar(X, Y, Legend(5), Bar Style("Float"), Label("Label by Value"))
	),
	SendToReport(
		Dispatch({"Line"}, "", OutlineBox, {Close(0)}),
		Dispatch({"Bar"}, "", OutlineBox, {Close(0)}),
		Dispatch(
			{},
			"400",
			ScaleBox,
			{Legend Model(5, Properties(0, {Line Width(0)}, Item ID("Mean", 1)))}
		),
		Dispatch(
			{},
			"Graph Builder",
			FrameBox,
			{DispatchSeg(BarSeg(1), {Set Width Proportion(-1)})}
		)
	)
)
					
				
			
			
				
	-Jarmo