Look up the Cookson repeater and Kalthoff repeater. Both pre-date even the Girandoni air rifle. The Kalthoff does by a century, along with the Lorenzoni repeating pistol. Can’t say I knew that before this morning.
Yes, they predated, but some were pistols and others were rifles/muskets which saw only token military use due to expense and difficulty of maintenance. The Girondini was mentioned as an “assault” type weapon because there was some significant military use sparking international controversy, and the rifle’s magazine capacity was superior to prior and succeeding repeating rifles.
Here is a Youtube video about the Cookson flintlock:
Cookson volitional repeating flintlock
http://www.youtube.com/watch?v=cs4vjq6sW40