IMHO, the best answer is already here fore almost two years now:

Note you can specify a different Style Sheet for print which works better for Black and White – Ben Brocka♦ Jul 23 '12 at 10:50

Trying to find a 5-color scheme that'll work well in monochrome is far from ideal. You could make it work, but you'd probably end up with a palette that looks okayish in color or goodish in greyscale. Do you want to settle for -ish?

Assuming you are designing for web, you should not worry too much about the monochrome rendering of your color scheme, but design for full-color screens. You might want to take color blindness into consideration, but it's up to you to decide if that is worth the effort.

Once done, take a separate look at how a print of you site should look. This considers far more than color rendering alone:

• Is the font (size) okay for reading on paper?
• Does every image need to be printed?
• Are there some elements (e.g. ads) that should be omitted in print?
• Do you show hyperlinks like on screen or with the URL written out?
• Do you keep the same site width or are you goin to use the whole page width?
• Do you need the header and footer?

These are only a few things you should think about. Basically, print is a different medium on which you want to convey the same information. This asks for its own design. Whether that design is just an altered color palette or a total rearrangement of your content.

IMHO, the best answer is already here fore almost two years now:

Note you can specify a different Style Sheet for print which works better for Black and White – Ben Brocka♦ Jul 23 '12 at 10:50

Trying to find a 5-color scheme that'll work well in monochrome is far from ideal. You could make it work, but you'd probably end up with a palette that looks okayish in color or goodish in greyscale. Do you want to settle for -ish?

Assuming you are designing for web, you should not worry too much about the monochrome rendering of your color scheme, but design for full-color screens. You will need to consider color blindness and several packages can help with that. For example colorbrewer2.org.

Once done, take a separate look at how a print of you site should look. This considers far more than color rendering alone:

• Is the font (size) okay for reading on paper?
• Does every image need to be printed?
• Are there some elements (e.g. ads) that should be omitted in print?
• Do you show hyperlinks like on screen or with the URL written out?
• Do you keep the same site width or are you goin to use the whole page width?
• Do you need the header and footer?

These are only a few things you should think about. Basically, print is a different medium on which you want to convey the same information. This asks for its own design. Whether that design is just an altered color palette or a total rearrangement of your content.