Looking at what I have it looks like the .44 Henry used a .446 heeled bullet,
you could probably shoot the Ballard .44 Long in it.
The S&W .44 American is supposed to be a close center fire alternative.
From Wikipedia,
"The .44 Henry cartridge was used most notably in the Henry Model 1860 repeating rifle. This rifle was first used in the American Civil War, mainly by Union cavalry troops, although only in very limited numbers. It was also used by the very few Confederate troops who managed to capture one of these rifles along with a supply of ammunition, which was impossible to find in the Confederate south.
After the Civil War, the Henry cartridge was used in the Winchester Model 1866 rifles during the Russo-Turkish War (1877-1878) by the Turkish troops and in the Franco-Prussian War 1870/71 by the French.
In civilian models, Winchester Model 1866 rifles and carbines, Smith & Wesson No. 3 Revolvers, Colt Model 1860 Army long cylinder conversion and the Colt Model 1871-72 "Open Top" revolvers were available in .44 Henry. From 1875 until 1880, Colt produced Model 1873 Single Action Army's in .44 Henry to accommodate owners of Henry Model 1860 and Winchester Model 1866 rifles and carbines."
AntiqueSledMan.