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