Answer
Missouri, Kentucky, Virginia, North Carolina, Tennessee and Arkansas
https://en.wikipedia.org/wiki/President_Lincoln%27s_75,000_volunteers
https://en.wikipedia.org/wiki/Flags_of_the_Confederate_States_of_America
Edit - Yikes! So many different answers.
I note that the question asked about states from which Lincoln requested "divisions" to be raised, and I don't think his proclamation mentions the word "divisions" at all, but I don't think any players were misled by this.
The official answer assumes that Lincoln's call was intended for the governor of every state other than the seven that had already seceded. So those six states fall under the general terms of Lincoln's call.
However, as has been pointed out by the players, Lincoln's call said that the details would be communicated through the War Department. When you get down to the specifics, the details sent out by Secretary of War Simon Cameron listed specific numbers of regiments from specific states - and Tennessee and North Carolina were not included in Cameron's list. Virginia, Arkansas, Kentucky, and Missouri were included, and all of those eventually had a star on the 13-star Confederate flag, so I am accepting that answer.
By the way, Cameron apparently wasn't very good at math. He asked for a total of 87 regiments, with each regiment to consist of 1,780 men, and somehow concluded that that came to a total of 73,910 men.
No wonder Lincoln got rid of him less than a year later.
hoosier