We located the copy through the University of Tennessee.
(Click image to enlarge.)
There is also a political cartoon, "The Aerial Rights Division," showing black crows saying "Mix!" "Mix!" as they stand ready to barge in on some white birds' nest, with the white birds aghast at the concept. An accompanying short essay explains how birds keep to their own species and do not mix with other kinds of birds. (This would seem to imply that black people might be some other species than homo sapiens.)
In addition, via Miami University, here is a road sign that the group had posted in 1964, which was seen by civil rights workers touring the state as part of the "Freedom Summer" voter-registration campaign:
The sign bears the group's message: "States Rights - Racial Integrity."
The Citizens Councils were founded in Mississippi in 1954, in protest of the Brown v. Board of Education decision that declared public school segregation to be unconstitutional. The councils were dedicated to political activities opposing civil rights, notably boycotts of pro-civil rights individuals -- including a famous instance by the group in Barbour's town. It was distinguished from the Klan by the public self-identification of its members, and its image of suits and ties as opposed to white robes and nooses.
In a profile in the Weekly Standard, Barbour recalled the group in positive terms:
"You heard of the Citizens Councils? Up north they think it was like the KKK. Where I come from it was an organization of town leaders. In Yazoo City they passed a resolution that said anybody who started a chapter of the Klan would get their ass run out of town. If you had a job, you'd lose it. If you had a store, they'd see nobody shopped there. We didn't have a problem with the Klan in Yazoo City."
In an interview with me earlier, Barbour's spokesman insisted that the governor is not a racist.