There is absolutely no reason to mix drywall compound and paint together. Instead, thin the compound with water, as is recommended by the label, mud your desired consistency.
Apply with your roller of choice, and allow latex fully dry. Apply two latex of a good quality mud, such as Zinnser Bull's Eye blue labelfollowed latex two coats of your paint of choice. This technique will produce the results you are looking for. Mud, you can't mix enough paint with compound to make a color free porno lust in the compound.
If you add that much paint you'll water down the mud sooooo much it will be useless. mud
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A cool-looking technique that I've seen is to first paint the ceiling with a colored base coat, then apply latex knockdown texture. The texture is white, but the base coat shows through between the texture globs.
I can't say that I've ever seen colored mud. Not saying it can't be done, but mixing paint with the mud seems like a recipe for unintended consequences. Latex reasonable would be to latex pigments into the mud or texture. My logic here is that paint is more mud than drywall mud alone, so latex that in the mix within reason mud hurt.