Immigration would not be a big issue as immigrants are likely to remain a small portion of the Confederate population. With a large unskilled labour force, the country is unlike to attract immigrants in greater numbers than it did in OTL. The region is likely to be a net exporter of white and black labour to the north. As things stood, by 1910 Texas and Florida had immigrant population comprised mostly of migrant labourers that were mainly temporary migrants. Unlike the north, the south might continue to sponsor more open borders so as to alleviate labour shortages.
With the exception of Texas and Florida, most of the ex-Confederate states had very few immigrants between 1860 and 1990. Looking at the 1910 census, there were a total of 454,821 foreign-born individuals in the former confederacy, comprising 2% of the total population (compared with 25.8% of the northeast).
Of the immigrants in the ex-Confederacy in 1910, over half lived in Texas. Interestingly, 125,000 of Texas's foreign-born or 56.3% were born in Mexico, most being agricultural workers. Similarly, in Florida 42% of the foreign-born we're from Cuba and the West Indies mostly working in agriculture.
Percentage Foreign Born Population in 1910
Texas 6.2%
Florida 5.6%
Louisiana 3.2%
Virginia 1.3%
Arkansas 1.1%
All of the other ex-Confederate states had less than 1% of their population born abroad.
Unlike the Northeast, the Midwest or the West, most immigrants were not concentrated in urban areas. Only New Orleans, Tampa and Memphis had more than 5,000 foreign-born in 1910. New Orleans had 26,000 or 7.7% of it's population, Tampa with its 10,800 was unique insofar as 28% of the city was foreign-born. Memphis with it's 6,500 immigrants was the next largest immigrant city in the old Confederacy, but they were a mere 5% of the city's population. In Atlanta and Nashville only 2.9% and 2.7% of the population were immigrants by contrast.
By the standards of large immigrant countries,the ex-Confederacy would rank low on the list, far below the US and Canada. It would also have a far smaller foreign-born population in 1910 when compared to Argentina, Southern Brazil, Uruguay or Cuba. It ranks below Chile even where 4% were born abroad in 1907, but above Mexico where 0.8% were immigrants in 1910.