Who invented the magazine gun?

There's really no such thing as a "magazine gun", but i think i understand what it is you're asking.

From the creation of firearms right up to a few years predating the American civil war, virtually all long-bore weapons (muskets, rifles ect) were muzzle loaded flintlocks or percussion-cap that could only fire one shot before needing to be reloaded. The US calvalry began experimenting with pre-loaded cartridges and carbines (small rifles)during the war itself. After the Civil War, Tube-magazine lever actions were gaining popularity with the cavalry, as they were able to fire up to 7 shots without needing to reloaded, and they were small enough that it wasn't an extra burden on the horse with all the gear a cavalryman had to carry.

As for the first ever full size combat rifle to incorperate a "box" style magazine....i believe it was the Mauser M1893 invented by Dr. Paul von Mauser of Germany. It was also the first bolt action rifle, which many bolt action hunting rifles today are still based off of.