I became a Christian in 1980 and began attending a C&MA church soon after. As I grew in my faith, I later attended Toccoa Falls College, which is a C&MA school located in Georgia.
One might find it difficult to tie the church directly to any particular denomination, largely because they are primarily organized to support a worl missionary effort, which they have done for more than 100 years and have done it in a rather unique and effective approach. They support all their missionaries from the denomination, rather than have the missionaries struggle to support themselves. If there is another denomination that operates this way, I am unaware of it.
Toccoa Falls was an incredible strong college, but they did not teach an "Alliance" doctrine, per se, because thei r primary effort is in creating strong Christians who can defend the faith and serve our Lord effectively. I am still reaping benefits from attending there many years ago.
If you made me associate it with another church, I can guess that you would find some doctrinal similarities to the Nazarene church in the northern Alliance church, but the southern churches would probably lean more Calvinistic. Again, this is just a wild guess because I have the impression that each church takes on something of an identity of its own, with missions being the primary effort between them all. Perhaps, after all these years, it is still operating as something of a parachurch group. If I remember correctly, the founder, AB Simpson, started as a Presbyterian, but I remain rathe runaware as to how that would affect today's Alliance churches.
Hope this helps.