I'm not sure if this is the "right" way, but one way is to include a vector of colors in your package. For example, I created a package with a bunch of utility functions and vectors that I use in my work. One file in the package is called utility_vectors.r where I keep various objects, one of which is a vector of my school's colors. An analogous version for your colors would be:
@joels’s answer seems like a good one. If you want to go a bit further and create custom palettes and ggplot2 scales, I’ve found this blog post to be a great resource.