Implementation thoughts:
I'm imagining that a "combo count" value is kept and incremented each time an object with a New Combo marker is found. Combo colours are chosen by taking the mod-4 (or however many colours there happen to be) and looking up the corresponding RGB value in an array.
So:
Mask a 4-bit "combo offset value" onto the "hit object type" field. (Hang onto this separately when the beatmap is parsed.) When an object with a New Combo marker is encountered, in addition to incrementing the counter, offset it by this new value.
GUI ideas:
1. Lazy: Double-click the New Combo button to increment the combo offset. If it reaches ColourCount - 2, set it to 0.
2. Fancy: Make the New Combo button expand into a menu, showing a choice of colours.