I suggest you look at some historical maps. The New Mexico and Arizona Territory were historically divided horizontally not like the current division of the states to this day. The northern half of the territory was pro Union and the southern half was pro confederacy. Also the Axis and Allies style of mechanics for combat do not work the Civil War Era. Most regiments are just not completed killed off in battle. Rolling dice and eliminating whole regiments within a turn is far from historically accurate and does not capture the nature of the combat. IPCs in the Civil War Era do not make sense. Most of the southern states were rural and agricultural in nature. Also most of the Southern states did not like helping each other out. They were never really unified as the North was in their cause. Also the vast majority of Southerns would refuse any attacks made into the North. Robert Lee got into huge problems when he invaded the North. The Southerns just wanted to fight a purely defensive war. The South had better generals and better trained soldiers because by its rural nature most of the people who enlisted already knew how to fire a weapon and they knew their home territority.
The reason a successful Civil War style Axis and Allies does not exist, is because the mechanics do not translate to the appropriate time period. I suggest doing extensive research about the Civil War, including how battles were fought, and how the states interacted with each other, and etc…