I write about 50,000 words per year for The Immigrants' Civil War blog, so hard and fast rules can go out the door when I see I have written "Confederates" for the seventh time in a blog. Normally, while I will refer to "Southern states", I try to avoid using directional terms which group people based on geography. For example, using the term "Southern army" for those in the Confederate army seems to ignore the fact that tens of thousands of whites from the Southern states and more than 100,000 blacks from those same states fought for the Union.
I tend to use Union/Confederate most often.