Only by hand.
Assuming there are no other style changes in those cells (not bold, italics, thick borders, or other styles applied already),
- Change the background colors in the first two cells (A4 and A5 in your screenshot)
- Select those two cells
- Copy Style (found in the Format menu)
- Select all the other cells where you want the alternating color.
- Paste Style
- Then change A3 and the row near the bottom.
If you have other styles applied already, another way is to select every other row (4, 6, 8, etc), set the color, do the same for the other rows (5, 7, 9, etc), then select the rightmost column and set the color back to "none".