Indeed there was, at least by the Germans, Irish, and Scots, but not in any large numbers to my knowledge. The main reason people didn't wish to settle in the CSA was because they feared being evicted by the USA in the event of a Union victory in the Civil War. To my knowledge, the CSA never kicked out any immigrants, nor did the USA evict anyone who moved to the Confederate states during the Civil War after it reestablished control (Primarily because the USA didn't treat the CSA as having ever left the Union in the first place), but that didn't stop charter companies that moved settlers from looking to safer ports of call with large populations of their respective ethnic group.

In Texas, for example, the Germans (The largest minority culture in Texas at the time, and still have a large presence today), Poles, and Czechs almost unanimously voted against secession because they did not want to be evicted by the USA should the CSA lose the war. They did not impede the CSA, and the CSA generally honored their agreement with the US Government to settle there, but they never threw in their lot officially in order to save face. Immigration still occurred in small numbers, but was significantly stifled by the Union blockade at Galveston (The largest port in Texas).

Also, people don't like moving to a region that's in political turmoil.