Hi Kenny,
I used these (the type you have and the one with two spring arms) way back when. I did a couple things to help quiet them down: took out all the screws and used loc-tite on them; and tried to dampen any metal to metal contact/vibration--such as where the spring arm may ride against the quiver framework, or where the metal framework is secured to the metal that holds the arrow gripper. If I recall I used a thinpiece of rubber or leather to do this.
I have to be honest, as much as I love Bear bows-the spring arm quiver wasn't a favorite of mine. In addition to the noise, I had a couple that the hoods ended up rubbing against the bow, marring the riser. as much as I like the original look-I use a Great Northern on my Bear TD now and use the spring arm as an arrow holder for display. Maybe someone else will chime in with some better tips that I can offer.