I use ne with the terminal that comes with Xfce, and in the terminal's Preferences --> Colors tab, there's a Palette section. The palette is by default set to the usual 16 terminal colors, but you can select a different palette if you like. I go with dark pastels, and it looks really nice.
The ne syntax files contain references to those default terminal colors, and the terminal palette settings let you choose different custom colors for them if you like. If the terminal you're using has something similar, you might be able to fiddle around with the color choices and get them to look somewhat like Monokai.