We'll set your data up in a table, which is a special data structure that lets other objects that link to it expand as you add data.
The table is shown below. Column B has the dates, columns C and D have the values you are plotting, columns E and F contain data we'll use for our labels.
Column E has the formula
=IF(ROW()=ROW([Date])+ROWS([Date])-1,[@[Hours 1]],NA())
Column F has the similar formula
=IF(ROW()=ROW([Date])+ROWS([Date])-1,[@[Hours 2]],NA())
The funny notation with brackets is table structured referencing, which Excel should generate as you write the formulas. If not, you can just base your formulas on what I have here. [Date] refers to the whole column of values in the Date column. [@[Hours 1]] refers to the cell in the Hours 1 column that is in the same row as the cell with the formula.
These formulas put #N/A into all cells of columns E and F except the last row, which contain the same values from columns C and D. #N/A is another piece of magic, in that is is not plotted, and will not be encumbered with a stray data label. We're going to plot all the data in our (vertical) bar chart, put data labels only on the column E and F bars, but hide the E and F bars.
The top left chart below shows all of the data plotted, and data labels on the last two series. The top right chart shows the column E and F bars hidden, by formatting them with no fill.
In the bottom left chart I've moved the column E and F bars to the secondary axis, so they line up with the column C and D bars. the labels are too high, though, because the primary and secondary axes have different scales. In the bottom right chart I've fixed that by deleting the secondary vertical axis.
Now we'll see the magic of Tables for making a dynamic chart.
The first view below shows the original five-row data range and corresponding chart.
The second view shows the table expanded by a couple rows. The cells in columns E and F with values are now in the new last row. The chart has expanded to include the new dates, and the data labels are still over the last bars in the chart.