In 1863 Confederate agents met with French Emperor Napoleon III and gained his permission for two ironclads to be secretly built in France for service with the Confederate Navy, directly circumventing French law. Armament for the ironclads was purchased separately in the United Kingdom. The two ships were ordered through French arms dealer Lucien Arman under the names Cheops and Sphynx to help build a cover story about them being built for Egypt, but eventually American diplomatic staff in France became aware of the deception and successfully pressured France to cancel the sale. Arman then illegally sold Cheops to Prussia and Sphynx to Denmark during May/June 1864, who were then engaged in the Second Schleswig War. Prussia kept Cheops, but the sales negotiation for Sphynx broke down and in January 1865 it entered service with the Confederate Navy at Copenhagen and was renamed CSS Stonewall. Stonewall began taking on more crew members and supplies and moved towards the East Coast of the United States, but sprung a leak that saw it spend much of February and March 1865 undergoing repairs in Spain. By the time it arrived in Havana, Cuba, in May 1865 the American Civil War was all but over and Captain Thomas Jefferson Page decided to sell his ship to Spain for $16,000. The United States Navy was apparently quite concerned about the potential arrival of the CSS Stonewall off the East Coast of the United States, and it seems that there weren't many ships that could have fought it. Depending on how seaworthy the oceangoing ironclads of the United States Navy were (the USS Dictator and USS Puritan), the USS New Ironsides might be the only ship capable of fighting them. Where might the Sphynx/Stonewall and Cheops have gone if they had entered service with the Confederate Navy as planned? How might they have fared in a battle with the United States Navy, especially against its ironclads?
The United States had many surplus oceangoing ironclads, including the Onondaga (ironically enough, it was sold to France in 1867) and possibly the Miantonomoh.
Would these ships have made any difference, the Confederate Navy was already outgunned and outmatch by the Union Navy.
That assumes they would be used in a direct battle with the United States Navy. They could prove far more useful opening a hole in the blockade around the Confederacy or engaging in commerce raiding (see the Alabama Claims). By 1864 it's too late to change the outcome of the war, but it could cause some changes in naval planning going forwards. Perhaps maintaining an adequate United States Navy would remain a priority, especially if the ironclads start causing trouble off the East Coast.
The Confederacy also ordered two Laird Rams from Laird & Sons the United Kingdom in 1862 using the same cover story about an Egyptian naval purchase: the El Toussan (intended CSS North Carolina) and the El Monnassir (intended CSS Wivern). The ships were seized in 1863 due to American diplomatic pressure as a result of commerce raiding by the CSS Alabama (another Laird built ship) and eventually purchased outright by the Royal Navy, entering service as the HMS Scorpion and HMS Wivern, respectively. The Confederacy had not purchased armament for the ships prior to their seizure and so the Royal Navy had to do so when they entered service. The Laird Rams are a less likely choice for entering service with the Confederacy though due to the political system of the United Kingdom and the fact that Laird's previous sales to the Confederacy were causing high profile damage to the United States.
That was the cover story, so if the Egyptians weren't looking for ironclads people must have thought it was a plausible thing at the time.
I found some more interesting information here. It turns out that two Re d'Italia class ironclads were under construction for the Italian Navy during the American Civil War, the Re d'Italia and the Re di Portogallo. The United States Navy could acquire them if needed. Also, this article mentions how the Confederacy went about ordering the two British and two French ironclads, as well as plans for them to fight the United States Navy and even bombard New York City and Philadelphia. From the article: There's also this part from the same article: