Jefferson Davis personally wrote a letter to Pope Pius IX.

Wikipedia has its text, reproduced below

Richmond, September 23, 1863.

Very Venerable Sovereign Pontiff: The letters which you have written to the clergy of New Orleans and New York have been communicated to me, and I have read with emotion the deep grief therein expressed for the ruin and devastation caused by the war which is now being waged by the United States against the States and people which have selected me as their President, and your orders to your clergy to exhort the people to peace and charity. I am deeply sensible of the Christian charity which has impelled you to this reiterated appeal to the clergy. It is for this reason that I feel it my duty to express personally, and in the name of the Confederate States, our gratitude for such sentiments of Christian good feeling and love, and to assure Your Holiness that the people, threatened even on their own hearths with the most cruel oppression and terrible carnage, is desirous now, as it has always been, to see the end of this impious war; that we have addressed prayers to heaven for that issue which Your Holiness now desires; that we desire none of our enemy's possessions, but that we fight merely to resist the devastation of our country and the shedding of our best blood, and to force them to let us live in peace under the protection of our own institutions, and under our laws, which not only insure to every one the enjoyment of his temporal rights, but also the free exercise of his religion. I pray your Holiness to accept, on the part of myself and the people of the Confederate States, our sincere thanks for your efforts in favor of peace. May the Lord preserve the days of your Holiness, and keep you under his divine protection.   Jefferson Davis

You can find the letter from Pius IX to Jefferson Davis here (scroll down). Here is the text:

Illustrious and honorable sir, greeting: We have lately received with all kindness, as was meet, the gentlemen sent by your Excellency to present to us your letter dated on the 23d of last September. We have received certainly no small pleasure in learning both from these gentlemen and from your letter the feelings of gratification and of very warm appreciation with which you, illustrious and honorable sir, were moved when you first had knowledge written in October of the preceding year to the venerable brethren, John [Hughes], archbishop of New York, and John [Odin], archbishop of New Orleans, in which we again and again urged and exhorted those venerable brethren that because of their exemplary piety and episcopal zeal they should employ their most earnest efforts, in our name also, in order that the fatal civil war which had arisen in the States should end, and that the people of America might again enjoy mutual peace and concord, and love each other with mutual charity. And it has been very gratifying to us to recognize illustrious and honorable sir, that you and your people are animated by the same desire for peace and tranquillity, which we had so earnestly inculcated in our aforesaid letters to the venerable brethren above named. May it please God at the same time to make the other peoples of America and their rulers, considering seriously how cruel and how deplorable is this internecine war, would receive and embrace the counsels of peace and tranquillity. We indeed shall not cease with most fervent prayer to beseech God, the best and highest, and to implore Him to pour out the spirit of Christian love and peace upon all the people of America, and to rescue them from the great calamities with which they are afflicted. We, at the same time, beseech the God of pity to shed abroad upon you the light of His grace, and attach you to us by a perfect friendship.

Given at Rome at St. Peter’s on the 3d December, 1863, in the eighteenth year of our pontificate.

Illustrious and Hon. Jefferson Davis President of the Confederate States of America, Richmond

The main point of contention for some is that the pontiff addresses Davis as ""Illustrious" and more importantly "President of the Confederate States of America." Some go so far as to assert that this statement signifies diplomatic recognition of the Confederacy by the papacy, as well as support for the Confederacy. The reality is much more mundane: the pontiff wrote a form letter to Davis. In the text, the pontiff deplores the civil war and makes an appeal for peace. Then he signs the letter by copying what Davis wrote as his title. In no way does this constitute diplomatic recognition or a statement of support for the Confederacy. Another reason against this assertion is that Pius IX wrote similar letters to Abraham Lincoln. If we are to take a letter as an endorsement, then the pontiff would have to be endorsing both sides of the war--an obvious self-contradiction.

The Confederacy did get a lot of propaganda usage out of the pontiff's letter, but that is quite a different story. Given the Confederacy's hostility to Catholicism it is implausible in my opinion that Pius IX would have endorsed such a government (which isn't to say that the Union was all that pleasant toward Catholics either).

A number of other letters are reproduced on this forum thread, if you are interested.

Another note: the Papal States were unable to do much of anything other than try to deal with the ongoing process of Italian unification, and had lost the great majority of its territory in 1860-61--only controlling Rome itself at the time of Davis' letter. Outside of the propaganda value there was little to be gained from any potential papal endorsement.