I don't think Calculate Field is the best path to follow here. The contents of ClrCount and ClrOrder depends on several other rows, possibly spread out over the entire feature class. It might be possible to create some codeblock logic involving cursors, dictionaries et cetera to get it to work, but it will defintly be messy.
If you have an ArcInfo license check if the Find Identical tool would help you. That one together with some clever join might be what you need.
If not (or maybe even with ArcInfo license) I'd create a new script tool, using an update cursor with the color field as the sort field, and just step through the feature class twice.
First time to set the color order. (start at zero and increment until a new color is found, then reset).
The second pass I'd still sort on color as the primary sort field, but add the newly created color order as the second sort field using descending sort for that value. Then update all the ClrCount field to hold the highest ClrOrder value + 1 (since it was zero based).