I have created calendar overlays with the colors I want by overriding CSS. example following How can I change the color dropdown list item names. is it possible ? Screenshot attached.
I made a calendar in SharePoint 2013, where the user can select a category and e.G. category1 I changed the color to red.
So I only needed one Calender without the overlay stuff. If you need more information about it you can check my blogpost.
It is in German, but the scripts and the formular should work. You can give it a try, if this solution will work for you and test it in the SP2010 Environment.