Are you using the default color Office theme? How much does the rest of the spreadsheet depend on color?
Excel uses the six Accent colors for the default colors of the first six series. Then it uses darker shades of the accent colors for the next six series. Then lighter tints for series 13–18, then darker. This procedure should get you to light usable tints for the accent colors without throwing the rest of the spreadsheet into a psychedelic nightmare.
On the ribbon, go to Page Layout >> Colors (in themes). In the pop-up menu, with your current theme selected, go to the bottom of the pop-up and select "Customize Colors..."
In the "Edit Theme Colors' dialog box that now pops up, select the down arrow next to the Accent 1 color chip. Select "More Colors..."
On the Custom tab, change the Color model from RGB to HSL. In the Lum box enter the value 203 and hit OK. Repeat for the remaining five accent colors.
On the main Edit Theme Colors dialog, give the theme a name and click Save. Your chart should change to the lighter colors.
Luminance, in Excel, runs from 0 for pure black to 255 for pure white. Think of it as the total amount of light emitted by the red, green and blue LEDs. Or the total amount of light reflected from a surface. The value of 203 (80% of max) is important to us because if you go over that value, the scheme of Accent colors changes. At Lum=204 and above, all accent color variations (for your cell fills and border line colors) go to the dark side—you can only get darker shades. With Lum=203, the Accent color variations give you three lighter tints and two darker shades.
Using Lum=203 for the accent colors shouldn't create too jarring a change in the rest of the spreadsheet. Just use this custom theme before printing, if you want.