No, there is no way to change colors at this time in the ArcGIS.com map viewer.
Thanks,
Mike
It's been 11 years, still an issue.
Colors in chart elements have been supported since the June update. You'll see additional information the What's New post for June and also in this blog tutorial on using charts in pop-ups.
The chart colors can't be independently changed, rather when using styles rendered using multiple attributes, chart element colors in pop-ups automatically match the style colors.