I have no color training, but the Color Scheme Designer has helped me several times in the past. I looked it up for you, is now called paletton.com and seems to be free, which is good for nonprofits.
I am not affiliated in any way, just a happy user.
You can click on the tetrad (4 color scheme) and enter your two-plus-one existing colors. Now you will see a resonable default-proposal for a new, third color. Do not miss to look at the examples-tab, to see what it might mean for your website.
Once you get the hang of this tool, you can go to the free-style scheme and use shift-drag to fine-tune your new color (while looking at previews!).
If you are interested in a little theory, I found the older website at:
Here go to help and activate tooltips, then hover over the major color schemes (like mono or tetrad) to read some text on what it does to the perception and to the feelings of the users...
If you find those tooltips on the new website, I would like to hear about it.
Sorry about the limitation on web-only. When I needed our non-profit stuff prepared for print on paper, I received some very friendly help from these pros: http://www.dtpstudio.de/english/index.html
And one last link (I might get spam-filtered) with more theory because of "the transfer of digital images to print":
I also learnt some more about colors (and how they behave, coming from screen and web and expanding towards pring) while using the program Scribus (which is also free, and very much meant to produce print-ready output).
Just activating Color Management in Scribus and looking for (importing) professional color palettes (open Scribus but have no document open, then go > Edit > Colors... > Import) and then using Color Management to simulate paper-results on my screen has been really helpful.