Well William Brownlow of the Nashville Whig had his paper shut down and he was jailed by the Davis regime in October 1861. In 1863 he has released from jail and deported to the U.S. Does that count?
But fair is fair. Name a single newspaper editor in the North that was jailed for the duration of the war.
In fact the Davis regime was able to get by for the most part through threats and intimidation to keep the press in line. One possible reason may have been that many southern newspapers didn't survive the arrival of Northern troops and the fact that there wasn't as much disagreement over the war in the south as there was in the North.
"In 1863 he has released from jail and deported to the U.S"
deported to expel from a country
One has to be careful accepting non-sequitur's pronouncements about things like this. Here is one version of what happened to Brownlow:
Remaining, for awhile, unmolested at Knoxville, he [Brownlow] was finally taken away by his friends, and remained in concealment for some time in the mountains of Tennessee, until he was induced, by the offer of a safe escort out of the State to the North, to appear at the rebel military headquarters at Knoxville. Upon his arrival there, December 6th, 1861, he was arrested, on a civil process, for treason, and thrown into jail. After a month's confinement, he was released, only to be immediately re-arrested by military authority, and was kept under guard in his own house, expecting death, and suffering from severe illness, till March 3d, 1862. He was then sent, under escort, toward the Union lines at Nashville, which he finally entered on the 15th, having been detained ten days by the guerrilla force c e Colonel Morgan. Subsequently he made an extensive and successful tour of the Northern States, addressing large audiences in all the principal cities, and wrote an auto-biographical work, entitled, " Sketches of the Rise, Progress, and Decline of Secession, with a Narrative of Personal Adventure among the Rebels," which was published in Philadelphia. [Source: Brownlow]
That works out to a month in jail and three months of house arrest. Not what non-seq said.
Here are two links to other versions of Brownlow history. Link to Brownlow history and Another Brownlow history
For your information, the book Yankee Leviathan notes on page 144 that "only one paper (in Knoxville, Tennessee) seems to have been closed by national authorities [Confederate]; only one other (in Raleigh, North Carolina) was destroyed by mob action." The Tennessee paper was Brownlow's. However, some claim Brownlow's paper was shut down by state authorities, not national authorities (see Link).
Contrast that with what happened to newspapers and editors in the North during Lincoln's reign.