What I do is fire a single shot when not down the sight in between gunfights. That stops the vibration until the next time you ADS or switch back to it or exit a menu. Irritating but worth it for the health regen on my elemental siren.
XBL GT: LazarusNecrosis The best techniques are passed on by the survivors. --Gaiden Shinji 1E 490
For mine, if I fire it, then it doesn't vibrate again until I zoom or reload. When I'm actually firing it, I don't notice any additional rumble that other weapons don't already have. If it starts to bug me, I just use another weapon.
Jogurt attacks! Inflicts 1 point of damage on the Goblin. Goblin is defeated! Jogurt gains experience. ...it appears that Jogurt's level has increased to 1.